Exact travelling wave solutions for the Penrose-Fife Phase Field Model

TL;DR

This paper derives exact traveling wave solutions for the Penrose-Fife Phase Field Model, a key model in phase transition theory, revealing complex parameter dependencies despite simple solution forms.

Contribution

It provides the first known exact solutions for the Penrose-Fife model, advancing analytical understanding of phase transition dynamics.

Findings

Exact traveling wave solutions derived

Solutions depend complexly on model parameters

First explicit solutions for this model in literature

Abstract

The Penrose-Fife Phase Field Model is now a well-established model in the theory of phase transitions. 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 traveling 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.