Uniqueness in thermoelasticity of porous media with microtemperatures

Abstract

The problem determined by thermoelastic deformations when the internal energy is not positive definite, becomes ill-posed. We call that this kind of situation happens in the study of prestressed thermoelastic solids. Thus, it will be of interest to obtain qualitative properties of solutions in this case. In this note we prove the uniqueness of solutions for the linear thermo-poro-elasticity with microtemperatures theory, when the internal energy is not to be assumed to be positive definite. We use the energy arguments combined with the Lagrange identities.