Some generalizations of the Caginalp phase-field system

Abstract

Our aim in this article is to study generalizations of the Caginalp phase-field system based on a thermomechanical theory of deformable continua proposed by Green and Naghdi. In particular, we obtain well-posedness results and study the asymptotic and spatial behaviours of the solutions.

Keywords:

• Caginalp system
• thermoelasticity
• type II
• type III
• well-posedness
• asymptotic behaviour of the solutions
• spatial behaviour of the solutions

AMS Subject Classifications::

• 35K55
• 35J60
• 80A22

Acknowledgements

This article was initiated while A. Miranville was visiting the Universitat Politècnica de Catalunya in Terrassa. He wishes to thank this institution for its warm hospitality. The work of R. Quintanilla is supported by the project ‘Estudio Cualitativo de Problemas Termomecánicos’ (MTM2006-03706).