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  • 1
    Digitale Medien
    Digitale Medien
    Springer
    Zeitschrift für angewandte Mathematik und Physik 47 (1996), S. 527-538 
    ISSN: 1420-9039
    Schlagwort(e): 35K50 ; 35B20 ; 35B30 ; 35B40 ; Heat conduction ; continuous dependence ; decay estimate
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract Using an energy method we investigate the decay of end effects for a generalized heat conduction problem defined on a semi-infinite cylindrical region. With homogeneous Dirichlet conditions on the lateral surface of the cylinder it is shown that solutions either grow exponentially or decay exponentially in the distance from the finite end of the cylinder. The effect of perturbing the equation parameters is also investigated.
    Materialart: Digitale Medien
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  • 2
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 11 (1989), S. 71-77 
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We consider a three-dimensional hyperelastic cylinder in Ω = D × [0, ∞]. We study the asymptotic behaviour of the deformations of the cross-sections in an equilibrium state. In this case we show that the solutions either have exponential decay or exponential growth. We give some initial conditions such that the latter case occurs.
    Materialart: Digitale Medien
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  • 3
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 11 (1989), S. 805-819 
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We consider several elliptic boundary value problems for which there is an overspecification of data on the boundary of the domain. After reformulating the problems in an equivalent integral form, we use the alternate integral formulation to deduce that if a solution exists, then the domain must be an N-ball. Various Green's functions and classical boundary value problems of second, fourth and higher order are included among the problems considered here.
    Materialart: Digitale Medien
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  • 4
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 11 (1989), S. 317-329 
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this paper we establish the stability of the solution of the standard initial-boundary value problem of linear anisotropic thermoelasticity under perturbations of the initial time geometry and of the spatial geometry. This is done by deriving appropriate explicit a priori inequalities which permit us to bound in particular the L2 integral of the perturbation in terms of some well defined measure of the perturbation in the geometry.
    Materialart: Digitale Medien
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  • 5
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 433-448 
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this paper we are concerned with the development of criteria for stabilizing inherently unstable initial-boundary value problems under small errors in the geometry of the underlying domain. We consider in particular the initial-boundary-value problem for the backward heat equation assuming that some error has been made in characterizing the geometry of the domain under consideration. It is shown that solutions which belong to an appropriately defined constraint set depend continuously in L2 on errors in the geometry.
    Materialart: Digitale Medien
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  • 6
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 223-237 
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We study the differential-delay equation x′(t) = -αf(x(t-1)), where α is a positive parameter and f is an odd function which decays like x-r at infinity. In particular, we consider the case r ≤ 2, and prove the existence of periodic solutions with special symmetries which are different from previously known periodic solutions of minimal period 4. For r = 2 we prove sharp asymptotic estimates for the minimal periods of these solutions.Our results disprove a conjecture of R. D. Nussbaum.
    Materialart: Digitale Medien
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  • 7
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 210-222 
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Lower bounds for the eigenvalues of some elliptic equations and elliptic systems over bounded regions are obtained. The bounds are universal in that they depend only upon the volume of the region. Specific applications include the clamped plate, the buckling problem for the clamped plate and the equations of linear elasticity.Our results are consequences of extensions of the methods of Li and Yau (Comm. Mat. Phys. 88 (1983) 309-318) who obtained such results for the eigenvalues of the fixed membrane problem.
    Materialart: Digitale Medien
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  • 8
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 35-45 
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The equations of Bleustein and Green [2] are formulated in a way suitable to describe the convective instability which occurs when a layer of dipolar fluid is heated from below. The linear instability boundary is shown to coincide with the nonlinear stability curve and the critical Rayleigh numbers describing this boundary are found; in particular, the non-dimensional micro-length is found to always stabilize.
    Materialart: Digitale Medien
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  • 9
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 127-136 
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The present paper employs potential well arguments of a previous work by the authors [6] to obtain a sharp existence-nonexistence alternative for solutions to the linear heat equation subject to a non-linear boundary condition.
    Materialart: Digitale Medien
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  • 10
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 449-456 
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In the x-y plane, let Ω denote an annular domain bounded by the simple closed curves ⌜ and ⌜*, such that the capacity potential U in Ω satisfies ∣ ▽ U∣ = 1 on ⌜. Assuming ⌜* to be known, we obtain qualitative properties of ⌜. For example, the number of local maxima or minima of the y-co-ordinate relative to ⌜ cannot exceed the corresponding number for ⌜*.
    Materialart: Digitale Medien
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