Exponential stability and uniqueness in thermoelasticity with two temperatures

Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis

Volumn 11, Issue 1, 2004, Pages 57-68

  Quintanilla, R ^a  

^a UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

Spatial stability; Stability; Thermoelasticity with two temperatures; Uniqueness

Indexed keywords

EID: 4544242698     PISSN: 12013390     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (15)

1. K.A. Ames and B. Straughan, Non-Standard and Improperly Posed Problems, Academic Press, San Diego, 1997.
2. P.J. Chen and M.E. Gurtin, On a theory of heat involving two temperatures, Jour. Appl. Math. Phys. (ZAMP), 19, (1968) 614-627.
3. P.J. Chen, M.E. Gurtin and W. O. Williams, A note on non-simple heat conduction, Jour. Appl. Math. Phys. (ZAMP), 19, (1968) 969-970.
4. P.J. Chen, M.E. Gurtin and W. O. Williams, On the thermodynamics of non-simple elastic materials with two temperatures, Jour. Appl. Math. Phys. (ZAMP), 20, (1969) 107-112.
5. S. Chirita, and R. Quintanilla, Spatial decay estimates of Saint-Venant tipe in generalized thermoelasticity, Int. J. Engrg.Sci., 34, (1996) 299-311.
6. M.E. Gurtin and W. O. Williams, An axiomatic foundation for continuum thermodynamics, Arch. Rational Mech. Anal., 26, (1967) 83-117.
7. C.O. Horgan, L.E. Payne and L.T. Wheeler, Spatial decay estimates in transient heat conduction, Quart. Appl. Math., 42, (1984) 119-127.
8. D. Iesan, On the linear coupled thermoelasticity with two temperatures, Jour. Appl. Math. Phys. (ZAMP), 21, (1970) 383-391.
9. L.E. Payne, and J. C. Song, Growth and decay in generalized thermoelasticity, Int. J. Engrg.Sci., 40, (2002) 385-400.
10. R. Quintanilla, End effects in thermoelasticity, Mathematical Methods in Applied Sciences, 24, (2001) 93-102.
11. R. Quintanilla, Damping of end effects in a thermoelastic theory, Appl. Math. Letters, 14, (2001) 137-141.
12. R. Quintanilla, Spatial asymptotic behaviour in incremental thermoelasticity, Asymp. Anal., 27, (2001) 265-279.
13. R. Quintanilla, On the spatial decay for the dynamical problem of thermo-microstretch elastic solids, Int. Jour. Eng. Scie., 40, (2002) 109-121.
14. R. Quintanilla, Exponential stability for one-dimensional problem of swelling porous elastic soils with fluid saturation, Jour. Comp. Appl. Math., 145, (2002) 525-533.
15. W.E. Warren and P.J. Chen, Wave propagation in two temperatures theory of thermoelasticity, Acta Mech., 16, (1973) 83-117.