Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



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

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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Additional Information

Alain Miranville
Affiliation: Université de Poitiers Laboratoire de Mathématiques et Applications UMR CNRS 7348 - SP2MI Boulevard Marie et Pierre Curie - Téléport 2 F-86962 Chasseneuil Futuroscope Cedex, France
Email: Alain.Miranville@math.univ-poitiers.fr

DOI: https://doi.org/10.1090/S0033-569X-2013-01331-1
Keywords: Conserved phase-field model, type III heat conduction, well-posedness, exponential attractor, global attractor
Received by editor(s): February 7, 2012
Received by editor(s) in revised form: April 25, 2012
Published electronically: August 29, 2013
Article copyright: © Copyright 2013 Brown University
The copyright for this article reverts to public domain 28 years after publication.

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