On uniqueness and stability in generalized thermoelasticity
Author:
Hany H. Sherief
Journal:
Quart. Appl. Math. 44 (1987), 773-778
MSC:
Primary 73U05
DOI:
https://doi.org/10.1090/qam/872828
MathSciNet review:
872828
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: A uniqueness theorem for the equations of generalized thermoelasticity with one relaxation time, derived by Dhaliwal and Sherief [1], is proved. The stability of the null solution in the sense of Liapounov, measured by a suitable norm, is shown. The corresponding equations for a homogeneous isotropic material, derived by Lord and Shulman [2], are considered as a special case.
- Ranjit S. Dhaliwal and Hani H. Sherief, Generalized thermoelasticity for anisotropic media, Quart. Appl. Math. 38 (1980/81), no. 1, 1–8. MR 575828, DOI https://doi.org/10.1090/S0033-569X-1980-0575828-8
H. W. Lord and Y. Shulman, A generalized dynamical theory of thermoelasticity, J. Meeh. Phys. Solids 15, 299–309 (1967)
- M. A. Biot, Thermoelasticity and irreversible thermodynamics, J. Appl. Phys. 27 (1956), 240–253. MR 77441
J. Ignaczak, Uniqueness in generalized thermoelasticity, J. Thermal Stresses 2, 171–175 (1979)
H. H. Sherief and R. S. Dhaliwal, A uniqueness theorem and a variational principle for generalized thermoelasticity, J. Thermal Stresses 3, 223–230 (1980)
- J. H. Weiner, A uniqueness theorem for the coupled thermoelastic problem, Quart. Appl. Math. 15 (1957), 102–105. MR 88216, DOI https://doi.org/10.1090/S0033-569X-1957-88216-8
- Józef Ignaczak, A note on uniqueness in thermoelasticity with one relaxation time, J. Thermal Stresses 5 (1982), no. 3-4, 257–263. MR 695431, DOI https://doi.org/10.1080/01495738208942149
J. L. Ericksen, A thermo-kinetic view of elastic stability theory, Internat. J. Solids and Structures 2, 573–580 (1966)
J. L. Ericksen, Thermoelastic stability, Proc. Fifth U.S. Natl. Congr. Appl. Mech., 187–193 (1966)
R. J. Knops and L. E. Payne, On uniqueness and continuous dependence in dynamical problems of linear thermoelasticity, Internat. J. Solids and Structures 6, 1173–1184 (1970)
R. S. Dhaliwal and H. H. Sherief, Generalized thermoelasticity for anisotropic media, Quart. Appl. Math. 38, 1–8 (1980)
H. W. Lord and Y. Shulman, A generalized dynamical theory of thermoelasticity, J. Meeh. Phys. Solids 15, 299–309 (1967)
M. A. Biot, Thermoelasticity and irreversible thermodynamics, J. Appl. Phys. 27, 240–253 (1956)
J. Ignaczak, Uniqueness in generalized thermoelasticity, J. Thermal Stresses 2, 171–175 (1979)
H. H. Sherief and R. S. Dhaliwal, A uniqueness theorem and a variational principle for generalized thermoelasticity, J. Thermal Stresses 3, 223–230 (1980)
J. H. Weiner, A uniqueness theorem for the coupled thermoelastic problem, Quart. Appl. Math. 15, 102–105 (1957)
J. Ignaczak, A note on uniqueness in thermoelasticity with one relaxation time, J. Thermal Stresses 5, 257–263 (1982)
J. L. Ericksen, A thermo-kinetic view of elastic stability theory, Internat. J. Solids and Structures 2, 573–580 (1966)
J. L. Ericksen, Thermoelastic stability, Proc. Fifth U.S. Natl. Congr. Appl. Mech., 187–193 (1966)
R. J. Knops and L. E. Payne, On uniqueness and continuous dependence in dynamical problems of linear thermoelasticity, Internat. J. Solids and Structures 6, 1173–1184 (1970)
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC:
73U05
Retrieve articles in all journals
with MSC:
73U05
Additional Information
Article copyright:
© Copyright 1987
American Mathematical Society