Travelling wave solutions for the Penrose-Fife phase field model.

The concept of the Phase Field is currently widely used in the Theory of Phase Transitions and Material science. The Penrose-Fife phase field model is now a well-established model in these fields. In the course of study of this model both the rigorous mathematical results and approximate solutions were obtained. However, to the best of our knowledge, no exact solutions were given in the literature. In the present paper we give exact travelling wave solutions for this system. While the functional form of the solutions is rather simple, the dependence of solutions on the parameters of the model is quite complicated. Also, an interesting link between this model and the Convective-Viscous Cahn-Hilliard equation is established. [ABSTRACT FROM AUTHOR]