International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 10, Pages 617-623

Some remarks on growth and uniqueness in thermoelasticity

Ramón Quintanilla

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.


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.