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  • 1
    Electronic Resource
    Electronic Resource
    Phragmén-Lindelöf and continuous dependence type results in generalized heat conduction (1996)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 47 (1996), S. 527-538 
    Details
    ISSN: 1420-9039
    Keywords: 35K50 ; 35B20 ; 35B30 ; 35B40 ; Heat conduction ; continuous dependence ; decay estimate
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00914869
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  • 2
    Electronic Resource
    Electronic Resource
    Some remarks on Saint-Venant's principle (1989)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 11 (1989), S. 71-77 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670110105
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  • 3
    Electronic Resource
    Electronic Resource
    Duality theorems in some overdetermined boundary value problems (1989)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 11 (1989), S. 805-819 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670110606
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Continuous dependence on the time and spatial geometry for the equations of thermoelasticity (1989)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 11 (1989), S. 317-329 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670110302
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  • 5
    Electronic Resource
    Electronic Resource
    Continuous dependence on geometry for the backward heat equation (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 433-448 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670060126
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  • 6
    Electronic Resource
    Electronic Resource
    Asymptotic analysis of differential-delay equations and nonuniqueness of periodic solutions (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 223-237 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670070114
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  • 7
    Electronic Resource
    Electronic Resource
    Unrestricted lower bounds for eigenvalues for classes of elliptic equations and systems of equations with applications to problems in elasticity (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 210-222 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670070113
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  • 8
    Electronic Resource
    Electronic Resource
    Stability of a layer of dipolar fluid heated from below (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 35-45 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670090104
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  • 9
    Electronic Resource
    Electronic Resource
    A potential well theory for the heat equation with a nonlinear boundary condition (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 127-136 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670090111
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  • 10
    Electronic Resource
    Electronic Resource
    On the geometric form of free boundaries satisfying a bernoulli condition (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 449-456 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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 ⌜*.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670060127
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