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Attractor for a conserved phase-field system with hyperbolic heat conduction

✍ Scribed by Maurizio Grasselli; Vittorino Pata

Publisher
John Wiley and Sons
Year
2004
Tongue
English
Weight
153 KB
Volume
27
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

We consider a conserved phase‐field system of Caginalp type, characterized by the assumption that both the internal energy and the heat flux depend on the past history of the temperature and its gradient, respectively. The latter dependence is a law of Gurtin–Pipkin type, so that the equation ruling the temperature evolution is hyperbolic. Thus, the system consists of a hyperbolic integrodifferential equation coupled with a fourth‐order evolution equation for the phase‐field. This model, endowed with suitable boundary conditions, has already been analysed within the theory of dissipative dynamical systems, and the existence of an absorbing set has been obtained. Here we prove the existence of the universal attractor. Copyright © 2004 John Wiley & Sons, Ltd.

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