Asymptotic behavior of the   conserved Caginalp phase-field system   based onthe Maxwell-Cattaneo law

Alain Miranville

doi:10.3934/cpaa.2014.13.1971

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2014, Volume 13, Issue 5: 1971-1987. Doi: 10.3934/cpaa.2014.13.1971

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Asymptotic behavior of the conserved Caginalp phase-field system based on the Maxwell-Cattaneo law

Alain Miranville^1,

1.
Université de Poitiers, Laboratoire de Mathématiques et Applications, UMR CNRS 6086 - SP2MI, Boulevard Marie et Pierre Curie - Téléport 2, F-86962 Chasseneuil Futuroscope Cedex

Received: September 2013

Revised: September 2014

Published: September 2015

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Abstract

Our aim in this paper is to study the well-posedness and the asymptotic behavior, in terms of finite-dimensional attractors, for the conserved Caginalp phase-field system based on the Maxwell-Cattaneo law, instead of the usual Fourier law, for heat conduction. The system consists of the equation for the order parameter and that for the enthalpy, instead of the relative temperature or the thermal displacement variable.

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Mathematics Subject Classification: 35K55, 35L15.

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