Asymptotic Behavior of the Solutions to a Landau--Ginzburg System with Viscosity for Martensitic Phase Transitions in Shape Memory Alloys

Abstract

In this paper, we investigate the system of partial differential equations governing the dynamics of martensitic phase transitions in shape memory alloys under the presence of a (possibly small) viscous stress. The corresponding free energy is assumed in Landau--Ginzburg form and nonconvex as a function of the order parameter. Results concerning the asymptotic behavior of the solution as time tends to infinity are proved, and the compactness of the orbit is shown.