Limitations of the coupled/ quasi-static approximation in multi-dimensional linear thermoelasticity

References

• Esham , B. F. Jr and Weinacht , R. J. 1994 . Singular perturbations and coupled/quasi static approximation in linear thermoelasticity . Siam J. Math. Anal , 25 : 1521 – 1536 .
   Google Scholar
• Weinacht R. J. The Coupled/Quasi Static Approximation in One Dimensional Linear Thennoelasticity to appear
   Google Scholar
• Dafermos , C. M. 1968 . On the existence and the asymptotic stability of solutions to the equations of linear thermoelasticity . Arch. Rat. Mech. Anal , 29 : 241 – 271 .
   Web of Science ®Google Scholar
• Weinacht , R. J. and Esham, Jr , B. F. 1996 . “ Energy Estimates in Thermoelasticity ” . In Non linear Problems in Applied Mathematics Edited by: Angell , T. S. , Pamela Cook , L. , Kleinman , R. E. and Olmstead , W. E. 259 – 268 . Siam, Philadelphia in honor of Ivar Stakgold on his 70th Birthday
   Google Scholar
• Rivera , J. E. 1991 . Decomposition of the displacement vector field and decay rates in linear thermoelasticity . Siam J. Math. Anal , 24 : 390 – 406 .
   Google Scholar
• Day , W. A. 1981 . Justification ofthe uncoupled and quasi static approximation in a problem of dynamic thennoelasticity . Arch. Rational Mech. Anal , 77 : 387 – 396 .
   Google Scholar
• Day , W. A. 1982 . Further Justification of the uncoupled and quasi static approximations in thennoelasticity . Arch. Rational Mech. Anal , 79 : 85 – 95 .
   Google Scholar
• Day , W. A. 1984 . A comment on approximations to the temperature in dynamic linear thermoelasticity . Arch. Rational Mech. Anal , 85 : 237 – 250 .
   Google Scholar
• Day , W. A. 1985 . Heat conduction within linear thennoelasticity . Springer Tracts in Natural Philosophy , 30
   Google Scholar
• Boley , B. A and Weiner , J. H. 1960 . Theory of Thermal Stresses .
   Google Scholar
• Carlson , D. E. 1972 . Linear Thennoelasticity . Handbuch der Physik , 6a/2
   Google Scholar
• Chadwick , P. 1960 . Thermoelasticity: . The dynamic theory, in Progress in Solid Mechanics ,
   Google Scholar
• Friedman , A. 1969 . “ Partial Differential Equations ” . New York : Holt, Rinehart and Winston .
   Google Scholar
• Zeidler , E. 1990 . Nonlinear Functional Analysis and its Applications . 2/A
   Google Scholar
• Ladyzhenskaya , O. A. 1969 . “ The Mathematical Theory of Viscous Incompressible Flow ” . New York : Gordon and Breach .
   Google Scholar