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 w...

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Bibliographic Details
Published in:	Phase transitions Vol. 92; no. 4; pp. 367 - 384
Main Authors:	Mchedlov-Petrosyan, P. O., Davydov, L. N.
Format:	Journal Article
Language:	English
Published:	Abingdon Taylor & Francis 03-04-2019 Taylor & Francis Ltd
Subjects:	convective-viscous Cahn-Hilliard equation Dependence exact solution phase field model Phase transition Phase transitions Traveling waves travelling wave
Online Access:	Get full text
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Summary:	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.
ISSN:	0141-1594 1029-0338
DOI:	10.1080/01411594.2019.1586900