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  • 1995-1999  (4.512)
  • 1997  (1.462)
  • 1995  (3.050)
  • Life and Medical Sciences  (3.042)
  • Engineering  (1.470)
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  • 1
    Digitale Medien
    Digitale Medien
    Generalized linear elasticity in exterior domains. I: Radiation problems (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1469-1500 
    Details
    ISSN: 0170-4214
    Schlagwort(e): radiating solutions ; exterior boundary value problem in elasticity ; variable coefficients ; Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We use Hodge-Helmholtz decompositions of weighted Sobolev spaces to solve time-harmonic exterior-boundary value problems for perturbations of the (aδd+bdδ)-system (δ: the co-differential, a, b〉0). We prove, that a Fredholm alternative holds true, the eigensolutions decay polynomially at infinity, and that the positive eigenvalues do not accumulate. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 2
    Digitale Medien
    Digitale Medien
    The 2-D Neumann problem in an exterior domain bounded by closed and open curves (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1551-1562 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The Neumann problem for the Laplace equation in an exterior connected plane region bounded by closed and open curves is studied. The existence of classical solution is proved by potential theory. The problem is reduced to the Fredholm equation of the second kind, which is uniquely solvable. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 3
    Digitale Medien
    Digitale Medien
    Numerical methods for scattering problems by curved gratings at high frequencies (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1531-1549 
    Details
    ISSN: 0170-4214
    Schlagwort(e): gratings ; Helmholtz equation ; high frequencies ; geometric theory of diffraction ; transition regions ; finite element method ; error estimates ; Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A new numerical method is derived for the calculation of high-frequency asymptotic expansions of the scalar wave scattered by curved periodic structures. Optimal error estimates for this method are established. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
    Zusätzliches Material: 5 Ill.
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  • 4
    Digitale Medien
    Digitale Medien
    Classification of smooth solutions to 2×2 hyperbolic systems with boundary damping (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1563-1598 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We give a complete classification for breakdown in finite time or global existence of continuously differentiable solutions to hyperbolic systems of two first-order partial differential equations posed on a real bounded interval, with boundary damping and initial data of small magnitude. Structural bounds for the derivatives of the initial data which govern the behavior of the solution are brought to light. We isolate two classes of boundary damping: the strong damping forbids the solution to blow up after a time that we exhibit while the weak damping permits a late breakdown. The results are applied to nonlinear elasticity. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
    Zusätzliches Material: 4 Ill.
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  • 5
    Digitale Medien
    Digitale Medien
    Singular Stress Behavior in a Bonded Hereditarily-Elastic Aging Wedge. Part II: General Heredity (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 31-45 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: No Abstract
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  • 6
    Digitale Medien
    Digitale Medien
    On Representation Formulas and Radiation Conditions (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 133-150 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Solutions of linear elliptic partial differential equations in unbounded domains can be represented by boundary potentials if they satisfy certain conditions at infinity. These radiation conditions depend on the fundamental solution chosen for the integral representation. We prove some basic results about radiation conditions in a rather general framework.Fundamental solutions G are considered that are defined only on the complement of a compact set. It turns out, however, and we present examples for this, that the more interesting results only hold if G is defined on all of ∝n or if it is a Green function for an exterior boundary value problem. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.
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  • 7
    Digitale Medien
    Digitale Medien
    Attractors and Approximate Inertial Manifolds for the Generalized Benjamin-Bona-Mahony Equation (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 189-203 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In the present paper, we deal with the long time behaviour of solutions for the generalized Benjamin-Bona-Mahony equation. By a priori estimates methods, we show this equation possesses a global attractor in Hk for every integer k≥2, which has finite Hausdorff and fractal dimensions. We also construct approximate inertial manifolds such that every solution enters their thin neighbourhood in a finite time. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.
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  • 8
    Digitale Medien
    Digitale Medien
    Factorization of a class of matrices generated by Sommerfeld diffraction problems with oblique derivatives (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1185-1198 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: An explicit factorization of the Fourier symbol matrix functions generated by Sommerfeld diffraction problems with oblique derivatives is obtained. For this purpose a new prefactorization procedure is developed which makes use of factorization through weighted L2 spaces. These results yield a representation of a generalized inverse of the corresponding matrix Wiener-Hopf operator and the asymptotic behaviour of the solution at the edge of the screen. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 9
    Digitale Medien
    Digitale Medien
    On quasi-linear Schrödinger-Poisson systems (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1223-1238 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We study a high-field version of the periodic Schrödinger-Poisson system, for which the Poisson equation includes nonlinear terms corresponding to a field-dependent dielectric constant. Using a Galerkin scheme, we prove global existence and uniqueness, and present the matrix equations for the numerical evaluation of the potential. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 10
    Digitale Medien
    Digitale Medien
    A generalized temperature-dependent, non-Newtonian Hele-Shaw flow in injection and compression moulding (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1199-1222 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A generalized Hele-Shaw flow is derived and analysed in injection and compression moulding which contains non-isothermal and non-Newtonian rheological behaviour of the molten polymers as well as non-symmetric effects. The corresponding fixed domain formulations for the flow are investigated from a mathematical point of view. Different approaches for the determination of the temperature and some viscosity models are discussed. Together with an outline of the proposed solution algorithm special finite element techniques are described for the numerical treatment of this complex non-linear moving boundary problem. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
    Zusätzliches Material: 3 Ill.
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  • 11
    Digitale Medien
    Digitale Medien
    On the Validity of the degenerate Ginzburg - Landau equation (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1239-1256 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The Ginzburg-Landau equation which describes nonlinear modulation of the amplitude of the basic pattern does not give a good approximation when the Landau constant (which describes the influence of the nonlinearity) is small. In this paper a derivation of the so-called degenerate (or generalized) Ginzburg-Landau (dGL)-equation is given. It turns out that one can understand the dGL-equation as an example of a normal form of a co-dimension two bifurcation for parabolic PDEs. The main body of the paper is devoted to the proof of the validity of the dGL as an equation whose solution approximate the solution of the original problem. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 12
    Digitale Medien
    Digitale Medien
    The Dirichlet problem for Stokes equation in a domain exterior to an open surface (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1257-1269 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The paper deals with the Dirichlet problem for the Stokes linear equation in a domain exterior to an open surface. With the help of the theory of boundary integral (pseudo-differential) equations uniqueness and existence theorems are proved in the Bessel-potential and Besov spaces and Cα-smoothness (with α〈1/2) of solution is established in the neighbourhood of the boundary of the open surface. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 13
    Digitale Medien
    Digitale Medien
    Long-time behaviour of ferromagnetic spin chain equation: global attractor and its dimension (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1271-1281 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this paper the authors consider the initial boundary value problem of the ferromagnetic spin chain equation and prove the existence of the global attractor and finiteness of the Hausdorff and the fractal dimensions of the attractor. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 14
    Digitale Medien
    Digitale Medien
    On stationary Schrödinger-Poisson equations modelling an electron gas with reduced dimension (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1283-1312 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We regard the Schrödinger-Poisson system arising from the modelling of an electron gas with reduced dimension in a bounded up to three-dimensional domain and establish the method of steepest descent. The electrostatic potentials of the iteration scheme will converge uniformly on the spatial domain. To get this result we investigate the Schrödinger operator, the Fermi level and the quantum mechanical electron density operator for square integrable electrostatic potentials. On bounded sets of potentials the Fermi level is continuous and bounded, and the electron density operator is monotone and Lipschitz continuous. As a tool we develop a Riesz-Dunford functional calculus for semibounded self-adjoint operators using paths of integration which enclose a real half-axis. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 15
    Digitale Medien
    Digitale Medien
    Existence results for non-autonomous multiple-fragmentation models (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1313-1323 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We investigate an initial-value problem modelling fragmentation processes where particles split into two or more pieces at a rate, γ, that not only depends on the sizes of the particles involved but also on time. The existence of non-negative, mass-conserving solutions is established by considering a truncated version of an associated non-autonomous abstract Cauchy problem. The latter has solutions of the form u(t)=Un(t,t0)f, t≥t0, where f is the known data at some fixed time t0≥0 and {Un(t,s)}t0≤s≤t≤T is a uniformly continuous evolution system. A limit evolution system {U(t,s)}t0≤s≤t≤T is shown to exist. Depending on the form of the known data f at time t0, the scalar-valued function u, obtained from the limit evolution system via u(x, t)=[U(t, t0)f](x) for a.e. x〉0, t≥t0, is a solution of either the original initial-value problem or an integral version of this problem. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 16
    Digitale Medien
    Digitale Medien
    Global solutions of the Laplace equation with a nonlinear dynamical boundary condition (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1325-1333 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We study the boundedness and a priori bounds of global solutions of the problem Δu=0 in Ω×(0, T), (∂u/∂t) + (∂u/∂ν) = h(u) on ∂Ω×(0, T), where Ω is a bounded domain in ∝N, ν is the outer normal on ∂Ω and h is a superlinear function. As an application of our results we show the existence of sign-changing stationary solutions. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 17
    Digitale Medien
    Digitale Medien
    Spatial bounds and growth estimates for the heat equation with three relaxation times (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1335-1344 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this note we investigate spatial bounds for the heat conduction equation with three relaxation times. We use energy methods similar to those considered in the study of the backward parabolic heat equation. Finally, we show that for any positive choice of the coefficients we may take initial data for which the solution is unstable when we suppose that the body is bounded. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 18
    Digitale Medien
    Digitale Medien
    Continuous sedimentation of multi-component particles (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1345-1364 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Continuous sedimentation of solid particles in a liquid takes place in a clarifier-thickener unit, which has one feed inlet and two outlets. The process is vital in a waste water treatment plant, where the particles consist of several biological components. The concentrations of these are modelled by a one-dimensional system of conservation laws with source term. It is shown how a unique solution can be obtained, and how analytical solutions are used to form a conservative numerical algorithm. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
    Zusätzliches Material: 7 Ill.
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  • 19
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    Digitale Medien
    Subsonic solutions of hydrodynamic model for semiconductors (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1389-1410 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: This paper is concerned with the existence and uniqueness of the steady-state solution of hydrodynamic model for semiconductor devices. Boundary conditions are prescribed by vorticity on inflow boundary as well as by electron density, temperature, and normal component of electron velocity on whole boundary. If the ambient temperature is large, and if both vorticity on inflow boundary and the variation of density on boundary are small, a unique subsonic solution exists. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 20
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    Digitale Medien
    Asymptotic solution of a non-linear wave motion in an electron plasma (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1379-1388 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The theory of high-frequency waves has been used to calculate first and second-order asymptotic solutions for the propagation of non-linear waves in a cylindrical symmetric flow of an electron plasma. The behaviour of acceleration waves and weak shock waves has been analysed through these solutions and Whitham's rule for a weak shock wave on any wavelet has been confirmed through the first-order solution. The appearance of a weak shock wave on any wavelet has been determined and its strength, the location, and the speed of propagation have been found from the asymptotic solution presented in this paper. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
    Zusätzliches Material: 4 Ill.
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  • 21
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    Digitale Medien
    The amount of non-uniqueness for factored equations with Euler-Poisson-Darboux factors (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1449-1457 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Of concern are factored Euler-Poisson-Darboux equations of the type∏Nj=1(d2/dt2+(ρ/t)d/dt+Aj)u(t)=0,where, for example, Aj=-cjΔ, Δ being the Dirichlet Laplacian acting on L2(Ω), Ω⊂∝n, and 0〈c1〈…〈cN. More generally -Aj can be the square of the generator of a (C0) group on a Banach space. When the constant ρ is negative, the initial value problem for the factored EPD equation is ill-posed. Nevertheless, we determine how many initial conditions are necessary to guarantee uniqueness of a solution. This number jumps up as ρ crosses a negative integer from right to left. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 22
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    On Global Existence, Asymptotic Stability and Blowing Up of Solutions for Some Degenerate Non-linear Wave Equations of Kirchhoff Type with a Strong Dissipation (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 151-177 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We study on the initial-boundary value problem for some degenerate non-linear wave equations of Kirchhoff type with a strong dissipation:\documentclass{minimal} \begin{document} \[ u_{tt}=\left\| \nabla u\right\| ^{2\gamma }\Delta u-\Delta u_t=\left| u\right| ^\alpha u,\quad u(0)=u_0,\;u_t(0)=u_1,\;u|_{\partial \Omega }=0. \] \end{document}When the initial energy $E(u_0,u_1)\equiv \left\| u_1\right\| ⁁2+\frac 1{\gamma +1}\left\| \nabla u_0\right\| ⁁{2(\gamma +1)}-\frac 2{\alpha+2}\left\| u_0\right\| _{\alpha +2}⁁{\alpha +2}$ associated with the equations is non-negative and small, a unique (weak) solution exists globally in time and has some decay properties. When the initial energy E(u0,u1) is negative, the solution blows up at some finite time. In the proof we use the ‘modified potential well’ and ‘Concavity’ methods. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.
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  • 23
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    Existence of a Classical Solution for a Multidimensional Filtration Problem (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 179-187 
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    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We prove existence, in a small time interval, of a classical solution having a regular free boundary, (i.e. the level set {u=0}) of a multidimensional filtration problem. The key point to get the regularity of the level set {u=0} is the proof of an a priori estimate for the L∞-norm of ut. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.
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  • 24
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    On Stationary Solutions of the Relativistic Vlasov-Maxwell System (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 667-677 
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    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We study stationary solutions of the relativistic Vlasov-Maxwell system of plasma physics which have a special form introduced (in the classical setting) by Rudykh, Sidorov and Sinitsy and establish their existence under suitable assumptions on the ansatz functions. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd. Math. Meth. Appl. Sci., Vol. 20, 667-677 (1997).
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  • 25
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    Convergence of Solutions of the Landau Equations in the Collisionless Limit (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 679-688 
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    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: This paper addresses the question: when the frequency of collisions vanishes, will the solutions of the Landau system converge to the solutions of the Vlasov system? We give a positive answer to the question for solutions satisfying certain regularity conditions. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd. Math. Meth. Appl. Sci., Vol. 20, 679-688 (1997).
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    Analysis of a Non-hyperbolic System Modeling Two-phase Flows Part 1: The Effects of Diffusion and Relaxation (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 783-803 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The paper considers the non-linear stability of a non-hyperbolic system of conservation laws with both relaxation and diffusion, which is commonly used for the modeling of two-phase fluid flows. Global existence in time is proved for initial data with a sufficiently small H1 norm. This result heavily depends on the nice structure of the relaxation system, derived from the initial system by setting the relaxation variables to zero. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    The dam problem for non-linear Darcy's laws and non-linear leaky boundary conditions (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1045-1068 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The goal of this paper is to establish that even for strongly non-linear Darcy's laws and strongly non-linear leaky boundary conditions on the bottom of the reservoirs the fluid flow through a porous dam is a well-posed problem for which existence of a solution can be established. In a simple case we provide also the exact solution to the problem. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
    Zusätzliches Material: 2 Ill.
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    Convex domains with stationary hot spots (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1163-1169 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Consider the problem of heat flow in a convex domain in ∝n with Dirichlet boundary condition and constant initial temperature. We show that the solution has a fixed hot spot if the domain is invariant under the action of an essential symmetry group. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
    Zusätzliches Material: 1 Ill.
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    Exponential decay for the one-dimensional wave equation with internal pointwise damping (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1171-1183 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The paper considers a particular type of closed-loop for the wave equation in one space dimension with damping acting at an arbitrary internal point, for which the uniform stabilization with exponential decay rate is shown. Applications to chains of coupled strings are also discussed. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    A non-linear parabolic control problem with non-homogeneous boundary condition - convergence of Galerkin approximation (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1365-1377 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The paper is concerned with optimal control problem for a non-linear parabolic equation with non-homogenous boundary condition and quadratic cost. The control is acting in a nonlinear equation. We derive some results on the existence of optimal controls. Then we treat optimal control problem by Galerkin method and we prove the convergence of optimal values for approximated control problems to the one for the original problem. Finally, we apply the results to give a simple example. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    On a fractional partial differential equation with dominating linear part (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1427-1448 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: It is proved that there is a (weak) solution of the equationut=a*uxx+b*g(ux)x+f,on ∝+ (where * denotes convolution over (-∞, t)) such that ux is locally bounded. Emphasis is put on having the assumptions on the initial conditions as weak as possible. The kernels a and b are completely monotone and if a(t)=t-α, b(t)=t-β, and g(ξ)∼sign(ξ)∣ξ∣γ for large ξ, then the main assumption is that α〉(2γ+2)/(3γ+1)β+(2γ-2)/(3γ+1). © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Numerical solution of viscoplastic constitutive equations with internal state variables Part I: algorithms and implementation (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1411-1425 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: This article treats the initial-boundary-value problem of viscoplasticity using unified constitutive models without a yield surface. Semi-discretization with the finite element method (FEM) leads to a system of differential-algebraic equations (DAE) with strongly non-linear evolution equations for the internal state variables. A special family of partitioned Runge-Kutta methods is introduced which allows an efficient time integration of the semidiscrete system. Coefficients for methods of order one, two, and three are given. Finally, numerical results for some two- and three-dimensional examples using the model of Hart are presented. In a second part we will give the theoretical background and state a proof of convergence for the algorithm presented in this paper. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
    Zusätzliches Material: 8 Ill.
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    Asymptotic spatial homogeneity of solutions to conservation laws with memory in several space dimensions (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1459-1468 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We prove that any solution of the problem(u+K*u)t+∑ai(u)uxi=0 on (0,∞)×∝Nwith spatially periodic initial data converges to a constant provided some non-degeneracy conditions on the kernel K and the non-linear functions ai,i=1,…,N are imposed. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Generalized linear elasticity in exterior domains. II: low-frequency asymptotics (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1501-1530 
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    ISSN: 0170-4214
    Schlagwort(e): radiating solutions ; exterior boundary value problems in elasticity ; asymptotic expansions ; low-frequency behaviour ; Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We continue the study of the operators of generalized linear elasticity and investigate the behaviour of the solutions as the frequency tends to zero. We identify degenerate operators in terms of special solutions to the static problem which must be added to the usual Neumann series in order to describe the low frequency behaviour adequately. As a byproduct we construct solutions to the homogeneous static operator (‘spherical elastics’) which generalize the spherical harmonics and give rise to a ‘spherical elastics expansion’. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Half-space Fourier transform in application to non-linear hyperbolic initial-boundary-value problem: low regularity solutions (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1599-1616 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The Dirichlet initial-boundary-value problem in the half-space ∝t×∝3+ for a non-linear hyperbolic system is studied. About the nonlinearity the null condition structure is imposed. Under the smallness conditions on the initial data the existence of low regularity solutions, on a given interval of time, is proved. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Clifford analysis on spheres and hyperbolae (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1617-1624 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We develop aspects of Clifford analysis over the sphere and hyperbolae. We focus primarily on the hyperbola lying in the Minkowski type space ∝n,1. We show that in order to give a proper extension of basic results on Clifford analysis in Euclidean space to this context one needs to consider both hyperbolae lying in ∝n,1. We also introduce Bergman spaces of Lp left monogenic sections in this context and consider the decomposition of square integrable sections over suitable bundles constructed over subdomains of spheres and hyperbolae. The results presented here cover the necessary background to enable one to set up and solve boundary value problems for field-type equations over hyperbolae. In particular, one can study analogues of the Dirichlet problem for analogues of the Laplacian over hyperbolae and spheres. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Dissipative Feedback Synthesis for a Singularly Perturbed Model of a Piston Driven Flow of a Non-Newtonian Fluid (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 79-94 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The limiting behaviour of solutions of a system of singularly perturbed equations is studied. The goal is to construct a dissipative feedback control synthesis that stabilizes the prescribed output functional along trajectories of solutions. The results are applied to a singularly perturbed Johnson-Sagelman-Oldroyd model of shearing motions of a piston driven flow of a non-Newtonian fluid. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.
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    Boundary Integral Equation Method in the Steady State Oscillation Problems for Anisotropic Bodies (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 95-119 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The three-dimensional steady state oscillation problems of the elasticity theory for homogeneous anisotropic bodies are studied. By means of the limiting absortion principle the fundamental matrices maximally decaying at infinity are constructed and the generalized Sommerfeld-Kupradze type radiation conditions are formulated. Special functional spaces are introduced in which the basic and mixed exterior boundary value problems of the steady state oscillation theory have unique solutions for arbitrary values of the oscillation parameter. Existence theorems are proved by reduction of the original boundary value problems to equivalent boundary integral (pseudodifferential) equations. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.
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    Error Estimates for the Boundary Element Approximation of a Contact Problem in Elasticity (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 205-217 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The two-dimensional frictionless contact problem of linear isotropic elasticity in the half-space is treated as a boundary variational inequality involving the Poincare-Steklov operator and discretized by linear boundary elements. Quadratic growth of the energy near the solution is shown under weak regularity assumptions if the central axis of external forces intersects the boundary of the domain in a Lebesgue null set. Estimating the numerical range of the discrete Poincare-Steklov operator and properly modifying it, enables the application of an error estimate for semi-coercive variational inequalities. Optimal order of convergence is obtained in the underlying Sobolev space H1/2(∂Ω)2. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.
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    Korn's Inequalities for Junctions of Spatial Bodies and Thin Rods (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 219-243 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The dependence on the small parameter ε of constants in Korn's inequalities is investigated for domains which are obtained by joining thin rods to an elastic spatial body. The external ends of the rods are clamped. The asymptotic accuracy of the derived inequalities is achieved by certain distribution of weight multipliers and powers of ε in L2-norms of displacements and their derivatives while the introduced weights differ for longitudinal and transversal components of displacement fields in the rods. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.
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    Asymptotic Behaviour of Solutions to some Pseudoparabolic Equations (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 271-289 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The aim of this paper is to investigate the behaviour as t→∞ of solutions to the Cauchy problem ut-Δut-νΔu-(b, ∇u)=∇⋅F(u), u(x, 0)=u0(x), where ν〉0 is a fixed constant, t≥0, x∊∝n. First, we prove that if u is the solution to the linearized equation, i.e. with ∇⋅F(u)≡0, then u decays like a solution for the analogous problem to the heat equation. Moreover, the long-time behaviour of u is described by the heat kernel. Next, analogous results are established for the non-linear equation with some assumptions imposed on F, p, and the initial condition u0. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.
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    Finite Element Methods for the Stokes System in Three-Dimensional Exterior Domains (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 245-269 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The article treats the question of how to numerically solve the Dirichlet problem for the Stokes system in the exterior of a three-dimensional bounded Lipschitz domain. In a first step, the solution of this problem is approximated by functions solving the Stokes system in a truncated domain and satisfying a suitable artificial boundary condition on the outer boundary of this truncated domain. In a second step, this new problem is approximately solved in finite element spaces related to a graded mesh as introduced by Goldstein [Math. Comp., 36, 387-404 (1981)]. The difference between this finite element approximation and the exact solution of the exterior Stokes problem is estimated in the norm of suitable unweighted L2-Sobolev spaces. These estimates are analogous to corresponding results which are known for the Poisson equation. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.
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    Inverse Problems for Identification of Memory Kernels in Viscoelasticity (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 291-314 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Inverse problems for identification of the memory kernel in the linear constitutive stress-strain relation of Boltzmann type are reduced to a non-linear Volterra integral equation using Fourier's method for solving the direct problem. To this equation the contraction principle in weighted norms is applied. In this way global existence of a solution to the inverse problem is proved and stability estimates for it are derived. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Control of Matter Waves in Adjacent Potential Wells (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 369-381 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We consider exact controllability of a system of two Schrödinger equations. These represent matter waves in adjacent potential wells with different potentials, one zero, the other a positive constant V0. The problem is formulated as a simultaneous boundary controllability problem, with Dirichlet control. Estimates for the controls, including an observability inequality, are proved using multiplier techniques. Then the Hilbert uniqueness method is used to obtain the exact controllability result. If V0 is sufficiently small, there exists a time T^(V0) such that the system is exactly controllable in times T〉T^(V0). © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    On ‘Power-logarithmic’ Solutions to the Dirichlet Problem for the Stokes System in a Dihedral Angle (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 315-346 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The Dirichlet problem for the Stokes system in a dihedral angle is considered. An explicit description of special solutions to the homogeneous problem which have the form\documentclass{minimal} \begin{document} \begin{eqnarray*} U(x) &=&\left| x\right| ^\lambda \sum_{0\leq k\leq \kappa }\frac{(\log \left| x\right|)^{\kappa -k}}{(\kappa -k)!}u^{(k)}(x/\left| x\right|), \\ P(x) &=&\left| x\right| ^{\lambda -1}\sum_{0\leq k\leq \kappa }\frac{(\log \left| x\right|)^{\kappa -k}}{(\kappa -k)!}p^{(k)}(x/\left| x\right|) \end{eqnarray*} \end{document}is given. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    On the Heat Convection Equations with Dissipation Term in Regions with Moving Boundaries (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 347-368 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We consider an initial value problem for a system of equations describing the motion and the heat convection in a viscous and incompressible fluid which occupies a smooth region Ωt⊂∝3 depending on time.In the equation for the distribution of temperature in the fluid we take into account not only the convective term but also the term responsible for the dissipation of energy.We prove local in time existence and uniqueness of solutions of the considered problem, and global in time existence for sufficiently small data. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    The Solvability of Boundary Equations in Mixed Problems for Non-stationary Maxwell's System (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 425-448 
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    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The work deals with boundary equations appearing if non-stationary problems for Maxwell system are solved with the help of surface-retarded potentials. The solvability of these equations is proved in some functional spaces of Sobolev type. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    A New Algorithm in Electromagnetic Inverse Scattering Theory with an Application to Medical Imaging (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 385-401 
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    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We consider the electromagnetic inverse scattering problem of determining the index of refraction of an isotropic inhomogeneous medium from a knowledge of the total electric near field data. We consider both the case of scattering by an infinite inhomogeneous cylinder and a bounded inhomogeneous region in space. We conclude by giving an application of our method to the problem of imaging leukemia in the upper leg by means of microwaves. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Parabolic Problems and Boundary Integral Equations (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 449-459 
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    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Here we consider initial boundary value problems for parabolic equations in non-bounded (with respect to time) domains by using the single-layer potential. We discuss the solvability in anisotropic Hölder spaces of the boundary integral equations, to which original parabolic problems are reduced. We construct the special operators (regularizers) for these integral equations which transform them to equivalent integral Volterra equations of the second kind with weakly singular kernels. As a corollary we obtain the theorem about the classical solvability in anisotropic Hölder spaces for initial boundary value parabolic problems. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Adaptive Coupling and Fast Solution of FEM-BEM Equations for Parabolic-Elliptic Interface Problems (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 403-423 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this paper we prove an a posteriori error estimate for the symmetric coupling of finite elements and boundary elements applied to linear parabolic-elliptic interface problems. The discontinuous Galerkin method is used for the discretization in time. We present an adaptive algorithm for choosing the mesh size in space and time and we analyse the Hybrid Modified Conjugate Residual (HMCR) method as a solution method for the linear systems which arise. Computational results show that the number of HMCR-iterations grows slowly with the problem size. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Editorial: G. C. Hsiao on his 60th birthday (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 383-384 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: No Abstract
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    Difference Methods for Quasilinear 2D-diffusion Problems in Toroidal Configurations (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 477-493 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Implicit one-step difference methods for quasilinear parabolic initial boundary value problems in two space variables and in polar coordinates are considered. Problems of this kind are suitable for the description of diffusion processes in plasma physics. Therefore, because of its special physical interest the dependence of the coefficients both on the solution and on its space derivatives (the fluxes) is included. The first part of this paper deals with proving convergence of the discrete approximations for vanishing step sizes. For this purpose, bounds for the inverse difference operators have to be derived previously. The nonlinear systems arising from the discretizations have exactly one solution for all step sizes being sufficiently small. In the second part of the article numerical tests are performed. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
    Zusätzliches Material: 9 Ill.
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    On the Existence of Trapped Modes in Channels of Arbitrary Cross-section (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 521-545 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: This article establishes the existence of trapped-mode solutions of a linearized water-wave problem. The fluid occupies a symmetric horizontal channel that is uniform everywhere apart from a confined region which either contains a thin vertical plate spanning the depth of the channel or has indentations in the channel walls. A trapped mode corresponds to an eigenvalue of a non-local Neumann-Dirichlet operator for an elliptic boundary-value problem in the fluid domain. The existence of such an eigenvalue is established by generalizing previous results concerning spectral theory for differential operators to this non-local operator. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Classical Global Solutions for Non-linear Klein-Gordon-Schrödinger Equations (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 599-616 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The existence of the classical global solutions for the non-linear Klein-Gordon-Schrödinger equations is proved in H1-subcritical cases for space dimensions n≤5. For higher space dimensions 6≤n≤9, we will give a subsequent paper to deal with. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    On the Long-time Behaviour of Solutions to a Conservation Law with Memory (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 569-581 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We show that any solution of the scalar conservation law(u+k*u)t+σ(u)x=0starting from spatially periodic initial datum stabilizes to its integral mean as time goes to infinity. No convexity or ‘genuinely non-linear’ like conditions are assumed concerning σ. © 1997 by B. C. Teubner stuttgart-John Wiley & Sons Ltd.
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    Characteristic Symmetric Hyperbolic Systems with Dissipation: Global Existence and Asymptotics (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 583-597 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We consider the initial-boundary value problem for quasi-linear symmetric hyperbolic systems with dissipation and characteristic boundary of constant multiplicity. We investigate the global existence and decay property of small regular solutions in suitable functions spaces which take into account the loss of regularity in the normal direction to the characteristic boundary. We also show the existence, uniqueness and stability of the time periodic solutions. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Uniqueness for Unbounded Classical Solutions of the MHD Equations (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 617-623 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The uniqueness for unbounded classical solutions of the magnetohydrodynamic (MHD) equations in the whole space is investigated. Under suitable growth condition, it is shown that the solution to the initial value problem is unique. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Positive Steady-state Solutions of a Non-linear Reaction-Diffusion System (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 625-634 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The steady-state problem of the non-linear reaction-diffusion systemut-uxx=u(av-b),vt-vxx=cuis considered. The existence of positive steady-solutions is established by using a fixed point theorem in ordered Banach space. The uniqueness of ordered positive steady-state solutions and an application to the associated reaction-diffusion system are presented. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Sommerfeld Diffraction Problems with Oblique Derivatives (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 635-652 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A class of diffraction problems for the two-dimensional Helmholtz equation is studied where the boundary conditions on a canonical screen contain oblique derivatives. The problem in weak formulation is reduced to a system of pseudodifferential equations on a half-line. The Fredholm property is characterized in dependence of the parameters, index formulas are given, and, if necessary, a normalization of the problem is implemented. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons Ltd.
    Zusätzliches Material: 4 Ill.
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    Control and Game-Theoretical Treatment of a Cost-Security Model for Disarmament (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 653-666 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this paper a time-discrete dynamic model for the process of disarmament is investigated. The state variables of the system are costs and security values. We assume that the costs can be controlled, and we aim at reducing the costs to zero and achieving non-negative security values after a finite number of time steps. In the case where the opponents behave cooperatively this leads to the solution of a linear programming problem. If the opponents behave non-cooperatively, then a Nash equilibrium has to be determined under linear constraints. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd. Math. Meth. Appl. Sci., Vol. 20, 653-666 (1997).
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    On Weak Solutions to the Non-stationary van Roosbroeck's System with Discontinuous Permittivities (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 689-706 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this paper we prove the existence of a weak solution to the non-stationary drift-diffusion equations (van Roosbroeck's system) of semiconductor theory involving discontinuous permittivities. The proof is based on an approximation of these equations by a system with bounded non-linearities, deriving a priori estimates on the approximate solutions and then carrying out the passage to limit. The discussion is completed by some regularity results for the weak solution under consideration. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd. Math. Meth. Appl. Sci., Vol. 20, 689-706 (1997).
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    Study of the Free Streaming Operator in Slab Geometry in Dependence of the Boundary Conditions (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 717-736 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We study the free streaming operator T∧ in a slab domain with boundary conditions described by a linear matrix operator Λ acting between the ‘incoming’ and ‘outgoing’ particle fluxes. Under suitable assumptions on the entries of Λ, it is proved that the resolvent operator of T∧ is positive. It is proved also that T∧ is the generator of a positive strongly continuous semigroup, whose type depends on the norm of the entries of Λ. Some examples are given. In particular the case of Maxwell type boundary conditions is studied and the location of the spectrum of T∧ is improved. © 1997 by B. G. Teubner Stuttgart - John Wiley & Sons Ltd. Math. Meth. Appl. Sci., Vol. 20, 717-736 (1997).
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    Estimating ∇u in terms of div u, curl u, either (ν, u) or ν×u and the topology (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 737-744 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In the present paper we prove Cα-estimates for ∇u using components of boundary values of u, div u, curl u and quantities given by components of boundary values of u as well as boundary values of elements belonging to de Rhams cohomology modules. The vector field u is defined on a bounded set G¯⊂∝3, meanwhile the cohomology group will be defined with regard to ∝3-G. Our inequalities turn out to be a priori estimates concerning well-known boundary value problems for vector fields. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    A Two-dimensional Stationary Induction Heating Problem (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 759-766 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We consider in this paper a system of equations modelling a steady-state induction heating process for ‘two-dimensional geometries’. Existence of a solution is stated in W1,p(Ω) Sobolev spaces and is derived using the Leray-Schauder's fixed point theory. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    A Functional Model for Quantum Mechanics: Unbounded Operators (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 745-757 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We extend the recently developed Riesz-Clifford monogenic functional calculus (based on Clifford analysis) for a set of unbounded non-commuting operators. Connections with quantum mechanics are discussed. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    A Singular Problem in Electrolytes Theory (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 767-782 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Existence and nonexistence of solutions (both stationary and evolution) for a parabolic-elliptic system describing the electrodiffusion of ions are studied. The answers to some questions concerning a generalization of a problem posed by I. Rubinstein are given. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Asymptotics as t → + ∞ of a Solution to the Periodic Cauchy Problem for the Damped Boussinesq Equation (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 805-812 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: No Abstract
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    On a Non-symmetric Problem in Electrochemical Machining (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 841-854 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We consider a free boundary value problem arising from a non-symmetric problem of electrochemical machining (ECM). After a conformal mapping of the unknown domain the problem is transformed to a non-smooth non-linear Riemann-Hilbert problem for holomorphic functions in the complex unit disk. A special technique allows to remove the singularities in the boundary condition. Utilizing existence results for smooth non-orientable Riemann-Hilbert problems, existence and uniqueness of a solution are shown. Finally, we propose an iterative method of Newton type for the effective numerical computation of the free boundary of the anode and present some test results. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    The Impedance Boundary Value Problem for the Helmholtz Equation in a Half-Plane (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 813-840 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We prove unique existence of solution for the impedance (or third) boundary value problem for the Helmholtz equation in a half-plane with arbitrary L∞ boundary data. This problem is of interest as a model of outdoor sound propagation over inhomogeneous flat terrain and as a model of rough surface scattering. To formulate the problem and prove uniqueness of solution we introduce a novel radiation condition, a generalization of that used in plane wave scattering by one-dimensional diffraction gratings. To prove existence of solution and a limiting absorption principle we first reformulate the problem as an equivalent second kind boundary integral equation to which we apply a form of Fredholm alternative, utilizing recent results on the solvability of integral equations on the real line in [5]. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    On the Finiteness of the Number of Determining Elements for von Karman Evolution Equations (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 855-865 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We prove the existence of a wide collection of finite sets of functionals that completely determine the long-time behaviour of strong solutions to the von Karman evolution equations. This collection contains finite sets of determining modes, nodes and local volume averages. The approach presented relies on the concept of a completeness defect for a set of linear functionals and it involves some ideas from abstract approximation theory. Our method is general enough and also can be applied to other non-linear partial differential equations which are of second order in time. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    On a Boundary Value Problem of the Biharmonic Equation (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 867-883 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this paper, we study a system of biharmonic equations coupled by the boundary conditions. These boundary conditions contain some combinations of the values, div, curl, and grad. Applications in mathematical physics are possible and the investigations will be done with the help of hypercomplex methods. It is also the aim of the paper to demonstrate the application of Clifford analytic methods to the solution of boundary value problems. The results on a special boundary value problem for the biharmonic equation will be used for the investigation of some first-order systems of partial differential equations. We study a theoretical problem connected with the ∂¯-problem and the solution of a Beltrami system by using a fixed-point iteration. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    On the Dirichlet Problem for the Two-dimensional Biharmonic Equation (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 885-890 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Modified fundamental solutions are used to show that the system of boundary integral equations in a direct method for the interior Dirichlet problem for the two-dimensional biharmonic equation has at most one solution on any smooth closed boundary contour. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    A Singular Transmission Problem: Alfvenic Resonance in Plasmas (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 891-903 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The non-homogeneous magnetohydrodynamics equation is studied, with emphasis on the singularities due to Alfvén resonance. It is shown that for any arbitrary function defined on the singular set, there exists a unique solution of the problem coinciding with this function. Then the values on the singular set which correspond to the correct physical solution are determined proving that this is unique except for a discrete set of geometrical configurations. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    On a Class of Overdetermined Eigenvalue Problems (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 905-914 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this paper we present some new results of symmetry for inhomogeneous Dirichlet eigenvalue problems overdetermined by a condition involving the gradient of the first eigenfunction on the boundary. One specificity of the problem studied is the dependence of the equation and the boundary condition on the distance to the origin. The method of investigation is based on the use of continuous Steiner symmetrization together with some domain derivative tools. An application is given to the study of an overdetermined eigenvalue problem for a wedge-like membrane. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    A Linear Thermoelastic Plate Equation with Dirichlet Boundary Condition (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 915-932 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We consider the initial-boundary value problem for a linear thermoelastic plate equation and we prove that the energy associated to the system decays exponentially to zero as time goes to infinity. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    A Threshold Result for a Non-local Parabolic Equation (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 933-943 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this paper, we consider the Cauchy problem:(ECP)ut-Δu+p(x)u=u(x,t)∫∝3u2(y,t)/∣x-y∣dy; x∊∝3, t〉0,u(x, 0)=u0(x)≥0 x∊∝3, (0.2)The stationary problem for (ECP) is the famous Choquard-Pekar problem, and it has a unique positive solution ū(x) as long as p(x) is radial, continuous in ∝3, p(x)≥ā〉0, and lim∣x∣→∞p(x)=p¯〉0. In this paper, we prove that if the initial data 0≤u0(x)≤(≢)ū(x), then the corresponding solution u(x, t) exists globally and it tends to the zero steady-state solution as t→∞, if u0(x)≥(≢)ū(x), then the solution u(x,t) blows up in finite time. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    The Incompressible Limit and the Initial Layer of the Compressible Euler Equation in ∝n+ (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 945-958 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We consider the incompressible limit of the compressible Euler equation in the half-space ∝n+. It is proved that the solutions of the non-dimensionalized compressible Euler equation converge to the solution of the incompressible Euler equation when the Mach number tends to zero. If the initial data v∞0 do not satisfy the condition ‘∇⋅v∞0=0’, then the initial layer will appear. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Stability Analysis of Navier-Stokes Flows in Annuli (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 959-978 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We study the linearized stability of planer flows of incompressible, viscous fluid in two-dimensional annular domains. A certain family of steady, explicit solutions which have spiral streamlines are considered. The Navier-Stokes equations are linearized at these solutions and we show analytically or numerically that these solutions are stable to perturbation of steady states, whatever the Reynolds number or the aspect ratio of the annuli may be. Hopf bifurcations from them are also examined numerically. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Homogenization of a spectral problem for a pile foundation structure (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 979-988 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The subject of this paper is the study of free oscillations of a composite material consisting of an elastic medium and a large number of elastic piles periodically immersed in a part of the medium. The ends of piles lying on the boundary of the medium are clamped to a force-free rigid plate. Such a partially composite structure arises in pile foundation mechanics. Assuming that the period of pile structure tends to zero, we obtain the macroscopic equations for free oscillations by homogenization method and prove the corresponding convergence result. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 80
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    Rawlins' problem for half-plane diffraction: its generalized eigenfunctions with real wave numbers (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 989-1014 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: This paper deals with a famous diffraction problem for a single half-plane Σ: x〉0, y=0 as an obstacle and for some time-harmonic plane incident wave field. Rawlins in 1975 was the first to solve the mixed (Dirichlet/Neumann) boundary value problem for the scalar Helmholtz equation. He also was the first to solve the equivalent pair of coupled Wiener-Hopf equations explicitly by factoring their discontinuous 2×2 Fourier matrix symbol in 1980. Although for real wave numbers k the usual factorization procedure fails it will serve as the basis: Following the lines given by Ali Mehmeti in his habilitation thesis [1] for the (Dirichlet/Dirichlet) boundary value problem we combine the idea of integral path deforming along the branch cuts of the characteristic square root √(ξ2-k2) given in Meister's book [13] with the modern Wiener-Hopf method solution derived by Speck [24] explicitly in a H1+ε, ε≥0, Sobolev space setting. The symmetry of the intermediate spaces Hs, H-s, ∣s∣〈1 2, which is due to generalized factorization, plays a key role in deforming the Fourier integral paths in order to get Laplace transform representations of the generalized eigenfunctions of the problem. As a remarkable fact 0〈ε〈¼ must hold here. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Spectral theory for the wave equation in two adjacent wedges (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1015-1044 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Consider the two adjacent rectangular wedges K1, K2 with common edge in the upper halfspace of ∝3 and the operator A (=-Laplacian multiplied by different constant coefficients a1, a2 in K1, K2, respectively) acting on a subspace of ∏2j=1L2(Kj). This subspace should consist of those sufficiently regular functions u=(u1,u2) satisfying the homogeneous Dirichlet boundary condition on the bottom of the upper halfspace. Moreover, the coincidence of u1 and u2 along the interface of the two wedges is prescribed as well as a transmission condition relating their first one-sided derivatives. We interpret the corresponding wave equation with A defining its spatial part as a simple model for wave propagation in two adjacent media with different material constants. In this paper it is shown (by Friedrichs' extension) that A is selfadjoint in a suitable Hilbert space. Applying the Fourier (-sine) transformations we reduce our problem with singularities along the z-axis to a non-singular Klein-Gordon equation in one space dimension with potential step. The resolvent, the limiting absorption principle and expansion in generalized eigenfunctions of A are derived (by Plancherel theory) from the corresponding results concerning the latter equation in one space dimension. An application of the spectral theorem for unbounded selfadjoint operators on Hilbert spaces yields the solution of the time dependent problem with prescribed initial data. The paper is concluded by a discussion of the relation between the physical geometry of the problem and its spectral properties. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Global existence for degenerate parabolic equations with a non-local forcing (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1069-1087 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We establish local existence and comparison for a model problem which incorporates the effects of non-linear diffusion, convection and reaction. The reaction term to be considered contains a non-local dependence, and we show that local solutions can be obtained via monotone limits of solutions to appropriately regularized problems. Utilizing this construction, it is further shown that, under conditions of either ‘weak reaction’ or ‘sufficiently small’ initial mass, solutions exist for all time. Finally, we provide an alternative analysis of global existence and investigate blow up in finite time for the case of power law diffusion and convection. These results show the extent to which the assumption of weak reaction may be relaxed and still obtain global existence. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Travelling waves in plasma sustained by a laser beam (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1089-1109 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: By means of the Conley connection index theory we prove existence of travelling wave solutions to a system of equations in a two temperature model of laser maintained plasma. These solutions describe locally the motion of plasma boundaries. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    Multidimensional characteristic Galerkin methods for hyperbolic systems (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1111-1125 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We consider characteristic Galerkin methods for the solution of hyperbolic systems of partial differential equations of first order. A new recipe for the construction of approximate evolution operators is given in order to derive consistent methods. With the help of semigroup theory we derive error estimates for classes of characteristic Galerkin methods. The theory is applied to the wave equation and also to the Euler equations of gas dynamics. In the latter case one can show that Fey's genuinely multidimensional method can be reinterpreted as a characteristic Galerkin method. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
    Zusätzliches Material: 4 Ill.
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    Stress L∞-estimates and the uniqueness problem for the quasistatic equations to the model of Bodner-Partom (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1127-1134 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: This paper proves the uniqueness result for global in time large solutions of quasistatic equations to an inelastic model of material behavior of metals, provided that an a priori L∞-estimation for the Cauchy stress tensor holds. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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    OBITUARY Peter Peet Silvester 1935-1996 (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 10 (1997), S. 1-1 
    Details
    ISSN: 0894-3370
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Elektrotechnik, Elektronik, Nachrichtentechnik
    Notizen: No Abstract
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    NUMERICAL SOLUTIONS FOR THE SCATTERED FIELDS FROM ROUGH SURFACES USING THE FULL WAVE GENERALIZED TELEGRAPHISTS' EQUATIONS (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 10 (1997), S. 83-99 
    Details
    ISSN: 0894-3370
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Elektrotechnik, Elektronik, Nachrichtentechnik
    Notizen: A numerical method is used to solve the integro-differential generalized telegraphists' equations for the total (single and multiple) diffusely scattered radiation wave amplitudes. These equations were derived using a full wave approach. The singularities of the scattering coefficients are removed on integrating by parts. A stationary phase approximation is used to obtain the far fields. The numerical solutions are obtained for one-dimensional deterministic surfaces. The numerical results for the total (single and multiple) diffusely scattered fields are in good agreement with the earlier single scatter analytical results when the maximum surface slope is less than 30 degrees. The earlier single scatter analytical solutions are based on the assumption that the total field impressed upon a rough surface is associated with the incident field only. This assumption is not made for the evaluation of the numerical results presented here. The earlier analytical results are in total agreement with the small perturbation results when the rough surface height and slopes are of the same order of smallness. © 1997 by John Wiley & Sons, Ltd.
    Zusätzliches Material: 15 Ill.
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    GENERALIZED MODAL SCATTERING MATRIX OF DISCONTINUITY-DISTORTED WAVEGUIDE MULTIPORT JUNCTIONS (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 10 (1997), S. 153-167 
    Details
    ISSN: 0894-3370
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Elektrotechnik, Elektronik, Nachrichtentechnik
    Notizen: A generalized modal scattering matrix formulation is presented for the calculation of discontinuity-distorted waveguide multiport junctions. Unlike common approaches based on three-plane mode-matching techniques, and modifications thereof, which calculate only the fundamental-mode scattering matrix, this algorithm computes the generalized modal scattering matrix of the junction. Therefore, the method allows the computation of components in which other structures are connected as closely as possible to the discontinuity-distorted junction as follows directly from the rigorous incorporation of all higher-order mode interactions. The method is demonstrated at three selected examples: the waveguide corner, the T-junction power divider and the orthomode transducer. Comparison with results obtained by other numerical techniques or measurements available from the literature are found to be in good agreement. © 1997 John Wiley & Sons, Ltd.
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    EFFICIENT HYBRID REPRESENTATION FORMULATION METHOD FOR COMPUTER SIMULATION OF LARGE CIRCUITS (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 10 (1997), S. 205-207 
    Details
    ISSN: 0894-3370
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Elektrotechnik, Elektronik, Nachrichtentechnik
    Notizen: A hybrid representation formulation approach is presented. It avoids some numerical inconveniences and was successfully used as an intermediate step to obtain the differential algebraic equations of PWL modelled VLSI circuits. © 1997 John Wiley & Sons, Ltd.
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    APPLICATION OF WAVELETS TO THE ANALYSIS OF ARBITRARY THIN-WIRE LOOP ANTENNAS AND SCATTERERS (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 10 (1997), S. 193-204 
    Details
    ISSN: 0894-3370
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Elektrotechnik, Elektronik, Nachrichtentechnik
    Notizen: An analysis of arbitrary thin-wire loop antennas and scatterers using periodic orthogonal wavelets is presented. The periodic orthogonal wavelet expansion is applied to solve the thin-wire version of the electric-field integral equation (EFIE). The curved solution domains are mapped into the definition domain [0, 1] of the periodic wavelets. The unknown current over each loop wire is expanded in terms of a basis derived from a periodic orthogonal wavelet through the maps between the curved integration domains and the interval [0,1]. The integral equation under study is converted into a sparse matrix equation by this technique. Numerical examples are provided for a variety of thin-wire loop antennas and scatterers. © 1997 John Wiley & Sons, Ltd.
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    A NUMERICAL STUDY OF BEAM WAVE INTERACTION DEVICES USING THE TRANSMISSION LINE MODELLING (TLM) METHOD (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 10 (1997), S. 231-243 
    Details
    ISSN: 0894-3370
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Elektrotechnik, Elektronik, Nachrichtentechnik
    Notizen: The suitability of the transmission line modelling method for studying field-particle interaction devices is assessed through an example of a simple two-cavity klystron amplifier. Two separate numerical studies are presented, covering both beam bunching in the buncher cavity and field generation in the catcher cavity. Also addressed are the possibility of modelling the effect of the finite thickness of the cavity wall and beam coupling. The modelling of these practical aspects has not only resulted in some important insights into the field-particle interaction problem, but also demonstrated that the computer code developed is a powerful and versatile design tool. © 1997 John Wiley & Sons, Ltd.
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    SPECTRAL-DOMAIN MODELLING OF SUPERCONDUCTING MICROSTRIP STRUCTURES (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 10 (1997), S. 217-229 
    Details
    ISSN: 0894-3370
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Elektrotechnik, Elektronik, Nachrichtentechnik
    Notizen: We present an analysis of thin microstrip superconducting structures in which the effects of the superconducting material, of finite complex conductivity and finite thickness, are taken into account through the concept of sheet impedance coupled with an extension of the Spectral Domain Immittance Approach. The effect of the magnetic field on the penetration depth in the superconductor is included by solving the Ginzburg-Landau equations within the thin-film approximation (t/λ0 ≪ 1). The state of the material is determined self-consistently in such a way that when the critical field is exceeded, the material systematically shifts from the superconducting to the normal state. Special attention is paid to the behaviour of the system in the neighbourhood of the critical temperature, T/Tc ≃ 1. We report that, in some cases, the propagation constant of a superconducting microstrip line attains a maximum when the real and imaginary parts of the conductivity are approximately equal. Numerical results for a microstrip line and a patch resonator are presented and compared with available data to document the validity of the approach. © 1997 John Wiley & Sons, Ltd.
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    Book Review: A posteriori error estimation and adaptive mesh-refinement techniques by Rüdiger Verfürth, Wiley-Teubner, 1996. ISBN 0-471-96795-5. No. of pages: 134. Price: £19.99 Hardback (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 10 (1997), S. 371-371 
    Details
    ISSN: 0894-3370
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Elektrotechnik, Elektronik, Nachrichtentechnik
    Notizen: No Abstract
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    APPLICATION OF CONFORMAL MAPPING IN MODELLING THE RESPONSE OF AN MSM PHOTODETECTOR (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 10 (1997), S. 71-82 
    Details
    ISSN: 0894-3370
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Elektrotechnik, Elektronik, Nachrichtentechnik
    Notizen: In this paper we present an efficient method for numerical solution of the transport equation of photogenerated carriers in MSM photodetectors. The method is based on conformal mapping of both the MSM photodetector structure and the system of transport equations into a new space. The mapping enables analytical calculation of the electric field, allowing one to take one of the co-ordinates as a parameter and thus reducing the problem to quasi-one-dimensional. In addition, the method of conformal mapping enables calculation of the normalized current response of a photodetector in the new space. © 1997 by John Wiley & Sons, Ltd.
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    Whole field computation using Monte Carlo method (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 10 (1997), S. 303-312 
    Details
    ISSN: 0894-3370
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Elektrotechnik, Elektronik, Nachrichtentechnik
    Notizen: Monte Carlo methods are generally known for solving field problems one point at a time, unlike other numerical methods such as the finite difference and finite element methods which provide the solution at all the grid nodes simultaneously. This paper provides a Monte Carlo technique for obtaining the solution everywhere at once. The technique uses absorbing Markov chains to obtain the transition probabilities for all of the grid nodes at once. The procedure is illustrated with some examples for homogeneous and inhomogeneous, rectangular and axisymmetric solution regions, and is found to be accurate. © 1997 John Wiley & Sons, Ltd.
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    A tabu search strategy for an efficient solution of linear systems in electromagnetic problems (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 10 (1997), S. 315-328 
    Details
    ISSN: 0894-3370
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Elektrotechnik, Elektronik, Nachrichtentechnik
    Notizen: A strategy is proposed to enhance the performance of some numerical methods used in the solution of electromagnetic problems. The strategy can be extended to any numerical method based on the partitioning of the spatial domain into elementary cells. Two different implementations of the strategy are compared: modified-reversed Cuthill-McKee and tabu search. While the former is well known, the latter is here applied for the first time to such problems. Their application is shown in conjunction with three different numerical methods: mode matching of complex MW circuits, finite difference solution of PDE and FEM analysis of microstrip lines. The efficiency and versatility of the approach is proved for each of the three numerical methods, reaching a reduction in the working times of up to 20 times. © 1997 John Wiley & Sons, Ltd.
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    IMPROVING MODULARITY IN OBJECT-ORIENTED FINITE ELEMENT PROGRAMMING (1997)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 13 (1997), S. 193-198 
    Details
    ISSN: 1069-8299
    Schlagwort(e): finite element method ; software engineering ; object-oriented programming ; Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: Making a finite element code easier to maintain is achieved by further modularizing it. Due to its two levels of modularity (of procedures and data), object-oriented programming is the method of choice. Its potential is investigated in two bottlenecks of finite element programming where so far it has not proved significantly more successful than classical Fortran programming. The first of these is the lack of adequate data structures between the analysis specifications and the basic objects of the finite element method, like the element and the node. This is solved by defining two classes of objects, namely problem and domain, with clearly differentiated specifications. The second gap deals with solving linear equation systems. Introducing an intermediate class UnassembledMatrix allows alternative storage/solving schemes to be implemented in a very flexible manner. © 1997 by John Wiley & Sons, Ltd.
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    TERMINATION CRITERIA IN ITERATIVE SOLUTION OF LARGE SCATTERING PROBLEMS USING INTEGRAL EQUATION METHODS (1997)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 13 (1997), S. 199-206 
    Details
    ISSN: 1069-8299
    Schlagwort(e): iterative solvers ; scattering analysis ; integral equations ; termination residual ; Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: Iterative methods are used increasingly for solution of the extremely large matrix equations generated by integral equation analysis of multi-wavelength frequency domain scattering. Although much cheaper than direct methods, the matrix solution remains the dominant cost, and is very costly. The criterion adopted for termination of the iteration can have a marked effect on this cost. We show that for large scattering problems a robust and rational prior choice of termination criterion can be made, based only on discretization. This allows confident use of a much larger termination residual than those commonly used, with consequent cost reduction. © 1997 by John Wiley & Sons, Ltd.
    Zusätzliches Material: 2 Ill.
    Materialart: Digitale Medien
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  • 99
    Digitale Medien
    Digitale Medien
    A MEMORY-EFFICIENT UNSTRUCTURED GRID REFINEMENT ALGORITHM FOR COMPUTATION OF 3D STEADY VISCOUS FLOWS (1997)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 13 (1997), S. 219-228 
    Details
    ISSN: 1069-8299
    Schlagwort(e): unstructured grids ; local grid refinement ; steady viscous flows ; Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: An algorithm for local refinement of unstructured grids for computation of 3D steady viscous flows is proposed. It is based on strict conventions for grid elements numbering that allows one to reduce memory requirements and to minimize the increase in the execution time for grid structure reconstruction. Additional savings in memory result from the fact that only grid refinement is allowed. The method requires about 20 integer words of storage per tetrahedron. The performance of the algorithm is illustrated by computation of several non-isothermal flow regimes in a horizontal epitaxial reactor. © 1997 by John Wiley & Sons, Ltd.
    Zusätzliches Material: 4 Ill.
    Materialart: Digitale Medien
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    Artikel (Nationallizenzen)
  • 100
    Digitale Medien
    Digitale Medien
    SUPERCONVERGENT PATCH RECOVERY IN PROBLEMS OF MIXED FORM (1997)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 13 (1997), S. 207-217 
    Details
    ISSN: 1069-8299
    Schlagwort(e): plates ; finite elements ; mixed method ; error estimation ; superconvergent patch recovery ; adaptivity ; Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: The superconvergent patch recovery (SPR technique) has been shown to be an effective postprocessing procedure in which an improved solution is obtained based on the original finite element solution. The technique was applied to second order problems with success, but the method has not yet been studied on problems posed in mixed form. This paper demonstrates that the technique can be applied to beam and plate bending problems, characterized by fourth order differential equations. The differential equation is here written as two coupled differential equations of second order leading to a mixed finite element procedure based on approximations of the moment and displacement fields. Two elements of mixed type are handled, namely a triangular plate element with constant moment field and a rectangular element with linearly varying bending moments. Numerical examples are given to show that the postprocessed solution is more accurate and has a higher rate of convergence. © 1997 by John Wiley & Sons, Ltd.
    Zusätzliches Material: 13 Ill.
    Materialart: Digitale Medien
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