A new dual approach for a class of phase transitions with memory: existence and long-time behaviour of solutions

In this paper we describe a class of phase transitions with thermal memory using a dual approach with respect to the temperature (and the free energy). More precisely, we use as state variables the phase parameter, the entropy (in place of the absolute temperature), and the history contribution of the entropy flux. The equations are recovered from a generalization of the principle of virtual power (to describe the evolution of the phases), including the effects of micro-motions responsible for the phase transition, and a rescalation of the internal energy balance (to describe the evolution of the entropy). We discuss thermodynamical consistency in terms of the properties of the involved energy functionals: the internal energy (in place of the free energy) and the pseudo-potential of dissipation. Hence, we prove existence of a solution (in a proper functional framework) for the resulting nonlinear integrodifferential PDE system. Finally, we discuss the long-time behaviour of solutions, characterizing the w-limit of trajectories.