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Well-posedness and long time behavior of a parabolic-hyperbolic phase-field system with singular potentials

Grasselli, M, Miranville, A, Pata, V and Zelik, S (2007) Well-posedness and long time behavior of a parabolic-hyperbolic phase-field system with singular potentials MATHEMATISCHE NACHRICHTEN, 280 (13-14). 1475 - 1509. ISSN 0025-584X

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Abstract

In this article, we study the long time behavior of a parabolic-hyperbolic system arising from the theory of phase transitions. This system consists of a parabolic equation governing the (relative) temperature which is nonlinearly coupled with a weakly damped semilinear hyperbolic equation ruling the evolution of the order parameter. The latter is a singular perturbation through an inertial term of the parabolic Allen-Cahn equation and it is characterized by the presence of a singular potential, e.g., of logarithmic type, instead of the classical double-well potential. We first prove the existence and uniqueness of strong solutions when the inertial coefficient epsilon is small enough. Then, we construct a robust family of exponential attractors (as epsilon goes to 0). (C) 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Item Type: Article
Uncontrolled Keywords: Science & Technology, Physical Sciences, Mathematics, phase-field systems, hyperbolic equations, strong solutions, robust exponential attractors, EXPONENTIAL ATTRACTORS, EQUATIONS, REGULARITY
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Divisions: Faculty of Engineering and Physical Sciences > Mathematics
Depositing User: Mr Adam Field
Date Deposited: 27 May 2010 14:40
Last Modified: 23 Sep 2013 18:32
URI: http://epubs.surrey.ac.uk/id/eprint/1419

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