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Uniqueness and growth of solutions in two-temperature generalized thermoelastic theories. (English) Zbl 1197.74031

Summary: We study modifications of the non-classical models of thermoelasticity, the one proposed Green and Lindsay and the one stated by Lord and Shulman, to two-temperature setting. We prove uniqueness results for the solutions of the systems of equations that model both theories for isotropic material. We also provide growth estimates for the solutions.

MSC:

74F05 Thermal effects in solid mechanics
74H25 Uniqueness of solutions of dynamical problems in solid mechanics
74H40 Long-time behavior of solutions for dynamical problems in solid mechanics
35Q74 PDEs in connection with mechanics of deformable solids
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[1] Dreyer, W., Continuum Mechanics and Thermodynamics 5 pp 3– (1993)
[2] Caviglia, G., International Journal of Nonlinear Mechanics 27 pp 251– (1992)
[3] Chandrasekharaiah, D.S., Applied Mechanics Review 39 pp 355– (1986) · Zbl 0588.73006
[4] Chandrasekharaiah, D.S., Applied Mechanics Review 51 pp 705– (1998)
[5] Hetnarski, R.B., Journal of Thermal Stresses 22 pp 451– (1999)
[6] Green, A.E., Journal of Thermal Stresses 15 pp 253– (1992)
[7] Green, A.E., Journal of Elasticity 31 pp 189– (1993) · Zbl 0784.73009
[8] Batra, R.C., Letters in Applied and Engineering Sciences 3 pp 97– (1975)
[9] Youssef, H.M., IMA Journal of Applied Mathematics 71 pp 383– (2006) · Zbl 1115.74019
[10] Green, A.E., Journal of Elasticity 2 pp 1– (1972) · Zbl 0775.73063
[11] Lord, H.W., Journal of Mechanics and Physics of Solids 15 pp 299– (1967) · Zbl 0156.22702
[12] Chen, P.J., Journal of Applied Mathematics and Physics (ZAMP) 19 pp 614– (1968) · Zbl 0159.15103
[13] Chen, P.J., Journal of Applied Mathematics and Physics (ZAMP) 19 pp 969– (1968)
[14] Chen, P.J., Journal of Applied Mathematics and Physics (ZAMP) 20 pp 107– (1969) · Zbl 0164.26104
[15] Warren, W.E., Acta Mechanica 16 pp 83– (1973) · Zbl 0251.73011
[16] Puri, P., International Journal of Engineering Science 44 pp 1113– (2006) · Zbl 1213.74161
[17] Quintanilla, R., Discrete and Continuous Dynamical Systems B 1 pp 463– (2001) · Zbl 1010.74016
[18] Quintanilla, R., Acta Mechanica 168 pp 61– (2004) · Zbl 1063.74026
[19] Racke, R., Mathematical Methods in the Applied Sciences 25 pp 409– (2002) · Zbl 1008.74027
[20] Iesan, D., Thermoelastic Deformations (1996)
[21] Quintanilla, R., Proceedings of the Royal Society of London A 456 pp 1419– (2000) · Zbl 0985.74018
[22] Quintanilla, R., International Journal of Mathematics and Mathematical Sciences pp 617– (2003) · Zbl 1045.35100
[23] Ames, K.A., Non-standard and Improperly Posed Problems (1997)
[24] Gilbarg, D., Elliptic Partial Differential Equations of Second Order (1977) · Zbl 0361.35003
[25] Knops, R.J., Archive for Rational Mechanics and Analysis 41 pp 363– (1971) · Zbl 0227.35017
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