A generalized conserved phase-field system based on type III heat conduction

Miranville, Alain

doi:10.1090/S0033-569X-2013-01331-1

Author: Alain Miranville
Journal: Quart. Appl. Math. 71 (2013), 755-771
MSC (2010): Primary 35K55, 35J60
DOI: https://doi.org/10.1090/S0033-569X-2013-01331-1
Published electronically: August 29, 2013
MathSciNet review: 3136994
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Abstract: In this paper, we are interested in the study of the asymptotic behavior, in terms of finite-dimensional attractors, of a generalization of the conserved phase-field system proposed by G. Caginalp. This model is based on a heat conduction law recently proposed in the context of thermoelasticity and known as type III law. In particular, we prove the existence of exponential attractors and, thus, of finite-dimensional global attractors.

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