Centre de Mathématiques et de Leurs Applications

Orateur : Elena BONETTI, Dep. Math. Université de Pavie

Titre : A new dual approach for phase transitions: existence and long-time behaviour of the solutions

Résumé :  Phase transitions  are a rich subject in the literature, starting from the well-known Stefan problem. They have many applications also in thermomechanics (as for SMA, damage, contact with adhesion, hydrogen storage...).
We deal with phenomena in which thermal memory is allowed and introduce ``an entropy approach'', which can be obtained by a dual formulation of the first principle,  and the new theory of micro-mouvements.
The resulting evolution PDE system is integrodifferential and highly nonlinear, mainly for the presence of different maximal monotone operators on the variables (non-smooth constraints).
We prove existence of a solution (in a proper functional framework) and   discuss the long-time behaviour of solutions holding on (0, +?) characterizing the ?-limit of trajectories.