Growth and uniqueness in thermoelasticity

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 456, Issue 1998, 2000, Pages 1419-1429

  Quintanilla, R ^a   Straughan, B ^a  

^a UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

Second sound; Solutions, growth in; Thermoelasticity; Thermoelasticity without energy dissipation; Uniqueness in

Indexed keywords

EID: 0000643354     PISSN: 13645021     EISSN: None     Source Type: Journal    
DOI: 10.1098/rspa.2000.0569     Document Type: Article

References (24)

1. Ames, K. A. & Payne, L. E. 1991 Stabilizing solutions of the equations of dynamical linear thermoelasticity backward in time. Stab. Appl. Analyt. Cont. Media 1, 243-260.
2. Ames, K. A. & Payne, L. E. 1994 Uniqueness and continuous dependence of solutions to a multidimensional thermoelastic contact problem. J. Elasticity 34, 139-148.
3. Ames, K. A. & Payne, L. E. 1995 Continuous dependence on initial-time geometry for a ther-moelastic system with sign-indefinite elasticities. J. Math. Analyt. Appl. 189, 693-714.
4. Ames, K. A. & Straughan, B. 1997 Non-standard and improperly posed problems. Mathematics in Science and Engineering Series, vol. 194. Academic.
5. Caviglia, G., Morro, A. fe Straughan, B. 1992 Thermoelasticity at cryogenic temperatures. Int. Jl Nonlin. Mech. 27, 251-263.
6. Chandrasekharaiah, D. S. 1996a A note on the uniqueness of solution in the linear theory of thermoelasticity without energy dissipation. J. Elasticity 43, 279-283.
7. Chandrasekharaiah, D. S. 19966 A uniqueness theorem in the theory of thermoelasticity without energy dissipation. J. Thermal Stresses 19, 267-272.
8. Dreyer, W. & Struchtrup, H. 1993 Heat pulse experiments revisited. Continuum Mech. Thermodyn. 5, 3-50.
9. Flavin, 3. & Rionero, S. 1996 Qualitative estimates for partial differential equations. Boca Raton, FL: CRC.
10. Gilbarg, D. & Trudinger, N. S. 1977 Elliptic partial differential equations of second order. Springer.
11. Green, A. E. & Naghdi, P. M. 1991 A re-examination of the basic postulates of thermomechanics. Proc. R. Soc. Land. A 432, 171-194.
12. Green, A. E. & Naghdi, P. M. 1992 On undamped heat waves in an elastic solid. J. Thermal Stresses 15, 253-264.
13. Green, A. E. & Naghdi, P. M. 1993 Thermoelasticity without energy-dissipation. J. Elasticity 31, 189-208.
14. Green, A. E. & Naghdi, P. M. 1995 A new thermoviscous theory for fluids. J. Non-Newtonian Fluid Mech. 56, 289-306.
15. lesan, D. 1998 On the theory of thermoelasticity without energy dissipation. J. Thermal Stresses 21, 295-307.
16. Jackson, H. E., Walker, C. T. & McNelly, T. F. 1970 Second sound in NaF. Phys. Rev. Lett. 25, 26-29.
17. Knops, R. J. & Payne, L. E. 1970 On uniqueness and continuous dependence in dynamical problems of linear thermoelasticity. Int. J. Solids Struct. 6, 1173-1184.
18. Knops, R. J. & Payne, L. E. 1971 Growth estimates for solutions of evolutionary equations in Hubert space with applications in elastodynamics. Arch. Ration. Mech. Analysis 41, 363-398.
19. Levine, H. A. 1970 On a theorem of Knops and Payne in dynamical linear thermoelasticity. Arch. Ration. Mech. Analysis 38, 290-307.
20. McNcIly, T. F., Rogers, S. J., Channin, D. J., Rollefson, R. J., Goubau, W. M., Schmidt, G. E., Krumhansl, J. A. & Pohl, R. O. 1970 Heat pulses in NaF: onset of second sound. Phys. Rev. Lett. 24, 100-102.
21. Nappa, L. 1998 Spatial decay estimates for the evolution equations of linear thermoelasticity without energy dissipation. J. Thermal Stresses 21, 581-592.
22. Quintanilla, R. 1999 On the spatial behaviour in thermoelasticity without energy dissipation. J. Thermal Stresses 22, 213-224.
23. Quintanilla, R. 2000 Existence and instability in thermoelasticity without energy dissipation. (In the press.)
24. Rionero, S. & Chirita, S. 1987 The Lagrange identity method in linear thermoelasticity. Int. Jl Engng Sei. 25, 935-947