International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 10, Pages 617-623
doi:10.1155/S0161171203108319
Some remarks on growth and uniqueness in thermoelasticity
Departamento Matematica Aplicada 2, Universidad Politecnica de Catalunya, Colon 11, Terrassa, Barcelona 08222, Spain
Received 13 August 2001; Revised 16 June 2002
Copyright © 2003 Ramón Quintanilla. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We use the Lagrange identity method and the logarithmic
convexity to obtain uniqueness and exponential growth of
solutions in the thermoelasticity of type III and
thermoelasticity without energy dissipation. As this is not the
first contribution of this kind in this theory, it is worth
remarking that the assumptions we use here are different from
those used in other previous contributions. We assume that the
elasticity tensor is positive semidefinite, but we allow that the
constitutive tensor of the entropy flux vector (kij), which
is a characteristic tensor in this theory, is not sign-definite.
The Lagrange identity method is used to obtain uniqueness in the
context of the thermoelasticity of type III. The fundamental key
to obtain exponential growth in the thermoelasticity without
energy dissipation is the use of a new functional. This
functional is inspired in that it is used when the elasticity
tensor is not sign-definite, but (kij) is positive definite.