Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

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.


References [Enhancements On Off] (What's this?)

  • [1] R. S. Dhaliwal and H. H. Sherief, Generalized thermoelasticity for anisotropic media, Quart. Appl. Math. 38, 1-8 (1980) MR 575828
  • [2] H. W. Lord and Y. Shulman, A generalized dynamical theory of thermoelasticity, J. Meeh. Phys. Solids 15, 299-309 (1967)
  • [3] M. A. Biot, Thermoelasticity and irreversible thermodynamics, J. Appl. Phys. 27, 240-253 (1956) MR 0077441
  • [4] J. Ignaczak, Uniqueness in generalized thermoelasticity, J. Thermal Stresses 2, 171-175 (1979)
  • [5] H. H. Sherief and R. S. Dhaliwal, A uniqueness theorem and a variational principle for generalized thermoelasticity, J. Thermal Stresses 3, 223-230 (1980)
  • [6] J. H. Weiner, A uniqueness theorem for the coupled thermoelastic problem, Quart. Appl. Math. 15, 102-105 (1957) MR 0088216
  • [7] J. Ignaczak, A note on uniqueness in thermoelasticity with one relaxation time, J. Thermal Stresses 5, 257-263 (1982) MR 695431
  • [8] J. L. Ericksen, A thermo-kinetic view of elastic stability theory, Internat. J. Solids and Structures 2, 573-580 (1966)
  • [9] J. L. Ericksen, Thermoelastic stability, Proc. Fifth U.S. Natl. Congr. Appl. Mech., 187-193 (1966)
  • [10] 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

DOI: https://doi.org/10.1090/qam/872828
Article copyright: © Copyright 1987 American Mathematical Society

American Mathematical Society