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
Full-text PDF Free Access
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Additional Information
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- Constantine M. Dafermos, On the existence and the asymptotic stability of solutions to the equations of linear thermoelasticity, Arch. Rational Mech. Anal. 29 (1968), 241–271. MR 233539, DOI https://doi.org/10.1007/BF00276727
- William Alan Day, Heat conduction within linear thermoelasticity, Springer Tracts in Natural Philosophy, vol. 30, Springer-Verlag, New York, 1985. MR 804043
B. F. Esham, Jr. and R. J. Weinacht, Hyperbolic-parabolic singular perturbations for quasi-linear equations, SIAM J. Math. Anal. 20, 1344–1365 (1989)
- B. F. Esham and R. J. Weinacht, Singular perturbations and the coupled/quasi-static approximation in linear thermoelasticity, SIAM J. Math. Anal. 25 (1994), no. 6, 1521–1536. MR 1302160, DOI https://doi.org/10.1137/S0036141093243708
F. R. Gantmacher, Theory of Matrices, 2 vols., Chelsea, New York, 1959
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B. A. Boley and J. W. Weiner, Theory of Thermal Stresses, John Wiley and Sons, New York, 1960
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)
W. A. Day, Heat conduction within linear thermoelasticity, in Springer Tracts in Natural Philosophy, 30, Springer-Verlag, Berlin, 1985
B. F. Esham, Jr. and R. J. Weinacht, Hyperbolic-parabolic singular perturbations for quasi-linear equations, SIAM J. Math. Anal. 20, 1344–1365 (1989)
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)
F. R. Gantmacher, Theory of Matrices, 2 vols., Chelsea, New York, 1959
G. C. Hsiao and R. J. Weinacht, A singularly perturbed Cauchy problem, J. Math. Anal. Appl. 71, 242–250 (1979)
R. Racke and Y. Shibata, Global smooth solutions and asymptotic stability in one-dimensional nonlinear thermoelasticity, Arch. Rat. Mech. Anal. 116, 1–34 (1991)
J. E. Rivera, Decomposition of the displacement vector field and decay rates in linear thermoelasticity, SIAM J. Math. Anal. 24, 390–406 (1991)
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)
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
E. Zeidler, Nonlinear Functional Analysis and its Applications, Vol. II/A, Springer-Verlag, New York, 1990
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© Copyright 2000
American Mathematical Society
