Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

Long-time behaviour for a model of phase-field type

Ph. Laurençota1

a1 Equipe de Mathématiques, CNRS URA 741, Université de Franche-Comté, Route de Gray, F-25030 Besançon Cedex, France

Abstract

In this paper, we study a model of phase-field type for the kinetics of phase transitions which was considered by Halperin, Hohenberg and Ma and which includes the phase-field equations. We study the well-posedness of the corresponding initial boundary value problem in an open bounded subset in space dimension lower than or equal to 3 and prove that, under suitable conditions, the long-time behaviour of the solutions to this problem is described by a maximal attractor.

(Received January 21 1994)

(Revised September 09 1994)