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A nonlinear system for irreversible phase changes

Published online by Cambridge University Press:  16 July 2009

Dominique Blanchard and
Hamid Ghidouche
Dominique Blanchard
Affiliation:
Service de Mathématiques, Laboratoire Mixte LCPC/CNRS, Laboratoire des Matériaux et des Structures du Génie Civil, 58 Boulevard Lefebvre, 75015 Paris, France
Hamid Ghidouche
Affiliation:
Département de Mathématiques, Université Paris 13, Avenue J.B. Clément, 93430 Villetaneuse, France
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Abstract

This paper is concerned with the mathematical study of a nonlinear system modelling an irreversible phase change problem. Uniqueness of the solution is proved using the accretivity of the system in (L1)2. Expressing one of the two unknowns as an explicit functional of the other reduces the system to a single nonlinear evolution equation and ultimately leads to an existence theorem.

In this paper the existence and uniqueness of the solution of a nonlinear system modelling some irreversible phase changes is established.

Information

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 1 , Issue 1 , March 1990, pp. 91 - 100
Copyright
Copyright © Cambridge University Press 1990

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References

Adams, R. 1975 Sobolev Spaces. Academic Press.Google Scholar
Attouch, H. 1979 Familles d'opérateurs maximaux monotones et mesurabilité. Annali Mat. Pura. Appli. 120, 35–111.CrossRefGoogle Scholar
Bénilan, Ph. 1975 Sur un problème d'évolution non monotone dans L 2(Ω). Internal Report, Université de Besançon, France.Google Scholar
Blanchard, D., Damlamian, A. & Ghidouche, H. A nonlinear system for phase change with dissipation. (To appear.)Google Scholar
Chalmers, B. 1977 Principles of Solidfication, Krieger.Google Scholar
Crandall, M. C. & Ligget, T. 1971 Generation of semigroups of nonlinear transformations in general Banach spaces. Amer. J. Math. 93, 265–440.CrossRefGoogle Scholar
Frémond, M. & Visintin, A. 1985 Dissipation dans le changement de phase, Surfusion, Changement de phase irréversible. C.R.A.S., Paris 301, (2, 18), 1265–1268.Google Scholar
Kinderlehrer, D. & Stampacchia, G. 1980 An Introduction to Variational Inequalities and their Applications, Academic Press.Google Scholar
Lions, J. L. 1969 Quelques Méthodes de Résolution Des Problèmes aux Limites non Linéaires, Dunod.Google Scholar
Visintin, A. 1985 Stefan problem with phase relaxation. I.M.A., J. Appl. Math. 34, 225–246.Google Scholar
Visintin, A. 1986 A new model for supercooling and superheating effects. I.M.A., J. Appl. 36, 141–157.Google Scholar