On the Asymptotic Behaviour of a Landau-Ginzburg Model for the Martensitic Phase Transitions in Shape Memory Alloys

Abstract

In this paper we report recent results on the asymptotic behaviour of a system of partial differential equations modelling the dynamics of martensitic phase transitions in shape memory alloys. In this model, the free energy is assumed to be in the Landau-Ginzburg form and nonconvex as function of the shear strain (which is the order parameter of the phase transitions), and the material is assumed to be linearly viscous. The system admits a unique global solution; in addition, the orbit is compact in suitable function spaces, and even the existence of a compact maximal attractor can be shown.