Some results on the well-posedness of an integro-differential Frémond model for shape memory alloys

This note deals with the nonlinear three-dimensional Frémond model for shape memory alloys in the case when the heat flux law contains a thermal memory term. The abstract formulation of the initial and boundary value problem for the resulting system of PDE's is considered. Existence and uniqueness of the solutions can be proved by exploiting a time discretization semi-implicit scheme, combined with an a priori estimate - passage to the limit procedure, as well as by performing suitable contracting estimates on the solutions.