Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



Existence and asymptotic analysis of a phase field model for supercooling

Authors: Olaf Klein, Fabio Luterotti and Riccarda Rossi
Journal: Quart. Appl. Math. 64 (2006), 291-319
MSC (2000): Primary 80A22; Secondary 28A33, 35K55
DOI: https://doi.org/10.1090/S0033-569X-06-01019-9
Published electronically: May 2, 2006
MathSciNet review: 2243865
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove an existence result for an initial-boundary value problem which models a perturbation of a phase transition phenomenon with supercooling effects. When the perturbation parameter goes to 0, an asymptotic analysis is performed. It leads to an existence result, in the framework of Young measures, for a slight modification of the original problem.

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Additional Information

Olaf Klein
Affiliation: Weierstrass Institute for Applied Analysis and Stochastics (WIAS), Mohrenstr. 39, D–10117 Berlin, Germany
Email: klein@wias-berlin.de

Fabio Luterotti
Affiliation: Dipartimento di Matematica, Università di Brescia, via Valotti 9, I–25133 Brescia, Italy
Email: luterott@ing.unibs.it

Riccarda Rossi
Affiliation: Dipartimento di Matematica, Università di Brescia, via Valotti 9, I–25133 Brescia, Italy
Email: riccarda.rossi@ing.unibs.it

DOI: https://doi.org/10.1090/S0033-569X-06-01019-9
Keywords: Phase field system, supercooling, doubly nonlinear equations, Young measures.
Received by editor(s): July 19, 2005
Published electronically: May 2, 2006
Additional Notes: The second and third author have been partially supported by the Italian COFIN project 2004 “Modellizzazione Matematica ed Analisi dei Problemi a Frontiera Libera”
Article copyright: © Copyright 2006 Brown University

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