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Sur un problème parabolique-elliptique

Published online by Cambridge University Press:  15 August 2002

Philippe Benilan  and
Petra Wittbold
Philippe Benilan
Affiliation:
Equipe de Mathématiques, UMR CNRS 6623, Université de Franche-Comté, 25030 Besançon Cedex, France.
Petra Wittbold
Affiliation:
UFR de Mathématiques et Informatique, 7 rue René Descartes, 67084 Strasbourg Cedex, France.
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Abstract

We prove existence (uniqueness is easy) of a weak solution to a boundary value problem for an equation like $(v-1)^+_t = v_{xx} + F(v)_x$ where the function $F: \Bbb R\rightarrow\Bbb R$ is onlysupposed to be locally lipschitz continuous. In order to replace the lack of compactness in t on v<1, we use nonlinear semigroup theory.

Keywords

Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 33 , Issue 1 , January 1999 , pp. 121 - 127
Copyright
© EDP Sciences, SMAI, 1999

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