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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References | Similar Articles | Additional Information

**[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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Additional Information

DOI:
https://doi.org/10.1090/qam/1770653

Article copyright:
© Copyright 2000
American Mathematical Society