Existence and large time behaviour for an entropy balance and linear thermal memory model for phase transitions

In this talk I will report on some recent results obtained in collaboration with E. Bonetti (Pavia), M. Fabrizio (Bologna), G. Gilardi (Pavia) and concerned with the dynamics of phase transitions. The (macroscopic) model is based on a balance law involving entropy and on a local balance of microforces which leads to a boundary value problem for a partial differential equation in the whole domain. Moreover, thermal memory effects are taken into account and the entropy flux is assumed to be linear with respect to the gradient of the absolute temperature. In this setting, one can consider the initial and boundary value problem for the coupled system of evolution equations and show the existence and uniqueness of a global solution. The stabilization and long time behaviour of such solution, as well as the structure of the omega limit set, will be discussed.