| Issue |
ESAIM: M2AN
Volume 33, Number 1, January Fabruary 1999
|
|
|---|---|---|
| Page(s) | 121 - 127 | |
| DOI | https://doi.org/10.1051/m2an:1999100 | |
| Published online | 15 August 2002 | |
Sur un problème parabolique-elliptique
1
Equipe de Mathématiques,
UMR CNRS 6623,
Université de Franche-Comté, 25030 Besançon Cedex, France.
2
UFR de Mathématiques et Informatique, 7 rue René Descartes,
67084 Strasbourg Cedex, France.
Received:
20
November
1997
We prove existence (uniqueness is easy) of a weak solution to a boundary value problem for an equation like 
where the function 
is only
supposed to be locally lipschitz continuous. In order to replace the lack of compactness in t on v<1, we use nonlinear semigroup theory.
Résumé
Nous prouvons l'existence (l'unicité est facile) d'une solution faible pour un problème aux limites associé à une équation du type où la fonction est seulement supposée localement lipschitzienne. Pour pallier au manque de compacité en t lorsque v<1, nous utilisons la théorie des semi-groupes non-linéaires.
Mathematics Subject Classification: 35K60 / 35K65 / 47H06 / 47H20
© EDP Sciences, SMAI, 1999
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