Existence of solutions for a mathematical model of structural phase transitions in shape memory alloys

Abstract

Abstract In this paper a thermomechanical model for the dynamics of structural phase transitions in the so‐called ‘shape memory alloys’ is developed. These materials exhibit rather spectacular hysteresis phenomena. The resulting mathematical model consists of a coupled and highly non‐linear system of partial differential equations reflecting the balance laws of linear momentum and energy. For an appropriate weak formulation the local‐in‐time existence of weak solutions is shown.