Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



A Caginalp phase-field system based on type III heat conduction with two temperatures

Authors: Alain Miranville and Ramon Quintanilla
Journal: Quart. Appl. Math. 74 (2016), 375-398
MSC (2010): Primary 35K55, 35J60, 80A22
DOI: https://doi.org/10.1090/qam/1430
Published electronically: March 16, 2016
MathSciNet review: 3505609
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Abstract: Our aim in this paper is to study a generalization of the Caginalp phase-field system based on the theory of type III thermomechanics with two temperatures for the heat conduction. In particular, we obtain well-posedness results and study the dissipativity of the associated solution operators. We consider here both regular and singular nonlinear terms. Furthermore, we endow the equations with two types of boundary conditions, namely, Dirichlet and Neumann. Finally, we study the spatial behavior of the solutions in a semi-infinite cylinder, when such solutions exist.

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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

Ramon Quintanilla
Affiliation: ETSEIAT-UPC, Departament de Matemàtiques, Colom 11, S-08222 Terrassa, Barcelona, Spain
Email: Ramon.Quintanilla@upc.edu

DOI: https://doi.org/10.1090/qam/1430
Keywords: Caginalp system, type III thermomechanics, two temperatures, well-posedness, dissipativity, spatial behavior, Phragm\'en-Lindel\"of alternative
Received by editor(s): May 15, 2015
Published electronically: March 16, 2016
Article copyright: © Copyright 2016 Brown University

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