Well-posedness of an integro-differential Fremond model for shape memory alloys

This paper deals with the nonlinear three-dimensional Fremond model for shape memory alloys in the case whern the heat flux contains some memory terms. The abstract formulation of the resulting initial-boundary PDE system is considered. Existence and uniqueness of solutions are proved by exploiting a semi-implicit time discretization scheme, combined with an a priori estimates passage to the limiti procedure as well by performing suitable contracting estimates on the solutions