Traveling Wave Solutions as Dynamic Phase Transitions in Shape Memory Alloys

Existence of travelling wave solutions for a system of nonlinear partial differential equations describing the evolution of shape memory alloys is shown. In the isothermal case we state a theorem which characterizes under which conditions travelling wave solutions exist. In the nonisothermal case we give an existence proof which uses the Conley index. To obtain this result the involved parameters have to be appropriately small.