Convergence and structural stability in thermoelasticity

Applied Mathematics and Computation

Volumn 135, Issue 2-3, 2003, Pages 287-300

  Quintanilla, Ramón ^a  

^a UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

Convergence; Structural stability; Thermoelasticity of types I, II and III

Indexed keywords

APPROXIMATION THEORY; ENERGY DISSIPATION; STRUCTURAL ANALYSIS; THERMOELASTICITY;

STRUCTURAL STABILITY;

CONVERGENCE OF NUMERICAL METHODS;

EID: 0037429583     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0096-3003(01)00331-9     Document Type: Article

References (26)

1. Ames K.A., Payne L.E. Continuous dependence on the initial time geometry for a thermoelastic system with sign-indefinite elasticities. J. Math. Anal. Appl. 189:1995;693-717.
2. Ames K.A., Straughan B. Non-Standard and Improperly Posed Problems. 1997;Academic Press, San Diego, CA.
3. Caviglia G., Morro A., Straughan B. Thermoelasticity at cryogenic temperatures. Internat. J. Non-Linear Mech. 27:1992;251-263.
4. Chandrasekharaiah D.S. Thermoelasticity with second sound: a review. Appl. Mech. Rev. 39:1986;355-376.
5. Chandrasekharaiah D.S. Hyperbolic thermoelasticity: a review of recent literature. Appl. Mech. Rev. 51:1998;705-729.
6. Dreyer W., Struchtrup H. Heat pulse experiments revisited. Continuum Mech. Thermodyn. 5:1993;3-50.
7. Green A.E., Naghdi P.M. A unified procedure for contruction of theories of deformable media. I. Classical continuum physics, II. Generalized continua, III. Mixtures of interacting continua. Proc. Roy. Soc. London Ser. A. 448:1995;335-356. (see also pp. 357-377, 379-388).
8. Green A.E., Naghdi P.M. A re-examination of the basic postulates of thermomechanics. Proc. Roy. Soc. London Ser. A. 432:1991;171-194.
9. Green A.E., Naghdi P.M. On undamped heat waves in an elastic solid. J. Thermal Stresses. 15:1992;253-264.
10. Green A.E., Naghdi P.M. Thermoelasticity without energy dissipation. J. Elasticity. 31:1993;189-208.
11. Green A.E., Naghdi P.M. A new thermoviscous theory for fluids. J. Non-Newtonian Fluid Mech. 56:1995;289-306.
12. Hetnarski R.B., Ignazack J. Generalized thermoelasticity. J. Thermal Stresses. 22:1999;451-470.
13. Iesan D., Scalia A. Thermoelastic Deformations. 1996;Kluwer Academic Publishers, Dordrecht.
14. Jou D., Vazquez C.-J., Lebon G. Extended Irreversible Thermodynamics. 1996;Springer, Berlin.
15. Knops R.J., Payne L.E. Continuous data dependence for the equations of classical elastodynamics. Math. Proc. Cambridge Philos. Soc. 66:1969;481-491.
16. Muller I., Ruggeri T. Rational and extended thermodynamics. 1998;Springer, New York.
17. Payne L.E., Song J.C. Continuous dependence on the initial-time geometry in generalized heat conduction. Math. Models Meth. Appl. Sci. 7:1997;125-138.
18. Payne L.E., Straughan B. Structural stability for the Darcy equations of flow in porous media. Proc. Roy. Soc. London Ser. A. 454:1998;1691-1698.
19. Payne L.E., Straughan B. Convergence and continuous dependence for the Brinkman-Forchheimer equations. Stud. Appl. Math. 102:1999;419-439.
20. Payne L.E., Straughan B. Convergence for the equations of Maxwell fluid. Stud. Appl. Math. 103:1999;267-278.
21. Payne L.E., Straughan B. Stability in the initial-time geometry problem for the Brinkman and Darcy equations of flow in porous media. J. Math. Pures Appl. 75:1996;225-271.
22. Payne L.E., Straughan B. Effects of errors in the initial-time geometry on the solution of the heat equation in an exterior domain. Quart. J. Mech. Appl. Math. 43:1990;75-86.
23. Quintanilla R., Straughan B. Growth and uniqueness in thermoelasticity. Proc. Roy. Soc. London Ser. A. 456:2000;1419-1429.
24. Quintanilla R. Logarithmic convexity in thermoelasticity of type III. Bermudez A., Gomez D., Hazard C., Joly P., Roberts J.E. Mathematical and Numerical Aspects of Wave Propagation. 2000;192-196 SIAM, Philadelphia, PA.
25. Quintanilla R. Existence in thermoelasticity without energy dissipation. J. Thermal Stresses. 25:2002;195-202.
26. R. Quintanilla, Some remarks on growth and uniqueness in thermoelasticity, Int. J. Math. Math. Sci., accepted