Existence and uniqueness of the solution to a 3D thermoviscoelastic system

Abstract

This paper presents results on existence and uniqueness of solutions to a three-dimensional thermoviscoelastic system.The constitutive relations of the model are recovered by a free energy functional and a pseudopotential of dissipation.Using a fixed point argument, combined with an a priori estimates-passage to the limit technique, we prove a local existence result for a related initial and boundary values problem.Hence, uniqueness of the solution is proved on the whole time interval, as well as positivity of the absolute temperature.