Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



The coupled/quasi-static approximation in one-dimensional linear thermoelasticity

Author: Richard J. Weinacht
Journal: Quart. Appl. Math. 58 (2000), 523-542
MSC: Primary 74H99; Secondary 35Q72, 74F05
DOI: https://doi.org/10.1090/qam/1770653
MathSciNet review: MR1770653
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  • [1] B. A. Boley and J. W. Weiner, Theory of Thermal Stresses, John Wiley and Sons, New York, 1960 MR 0112414
  • [2] C. M. Dafermos, On the existence and the asymptotic stability of solutions to the equations of linear thermoelasticity, Arch. Rat. Mech. Anal. 29, 241-271 (1968) MR 0233539
  • [3] W. A. Day, Heat conduction within linear thermoelasticity, in Springer Tracts in Natural Philosophy, 30, Springer-Verlag, Berlin, 1985 MR 804043
  • [4] B. F. Esham, Jr. and R. J. Weinacht, Hyperbolic-parabolic singular perturbations for quasi-linear equations, SIAM J. Math. Anal. 20, 1344-1365 (1989)
  • [5] B. F. Esham, Jr. and R. J. Weinacht, Singular perturbations and the coupled/quasi-static approximation in linear thermoelasticity, SIAM J. Math. Anal. 25, 1521-1536 (1994) MR 1302160
  • [6] F. R. Gantmacher, Theory of Matrices, 2 vols., Chelsea, New York, 1959
  • [7] G. C. Hsiao and R. J. Weinacht, A singularly perturbed Cauchy problem, J. Math. Anal. Appl. 71, 242-250 (1979) MR 545871
  • [8] R. Racke and Y. Shibata, Global smooth solutions and asymptotic stability in one-dimensional nonlinear thermoelasticity, Arch. Rat. Mech. Anal. 116, 1-34 (1991) MR 1130241
  • [9] J. E. Rivera, Decomposition of the displacement vector field and decay rates in linear thermoelasticity, SIAM J. Math. Anal. 24, 390-406 (1991) MR 1205533
  • [10] M. Slemrod, Global existence, uniqueness and asymptotic stability of classical smooth solutions in one-dimensional non-linear thermoelasticity, Arch. Rat. Mech. Anal. 75, 97-133 (1981) MR 629700
  • [11] R. J. Weinacht and B. F. Esham, Jr., Energy Estimates in Thermoelasticity, in Non-linear Problems in Applied Mathematics (in honor of Ivar Stakgold on his 70th Birthday), edited by T. S. Angell, L. Pamela Cook, R. E. Kleinman, and W. E. Olmstead, SIAM, Philadelphia, 1996, pp. 259-268 MR 2410620
  • [12] E. Zeidler, Nonlinear Functional Analysis and its Applications, Vol. II/A, Springer-Verlag, New York, 1990 MR 1033497

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DOI: https://doi.org/10.1090/qam/1770653
Article copyright: © Copyright 2000 American Mathematical Society

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