Partial differential equations
The method of differential contractions
[La méthode des contractions différentielles]

Présenté par : the Editorial Board

Monneau, Régis1
1 CERMICS, École des ponts ParisTech, Université Paris-Est, 6 et 8, avenue Blaise-Pascal, Cité Descartes, Champs-sur-Marne, 77455 Marne-la-Vallée cedex 2, France
Comptes Rendus. Mathématique, Tome 353 (2015) no. 2, pp. 143-147.

Dans cette Note, nous présentons une méthode simple et générale pour fabriquer des familles de contractions pour des équations aux dérivées partielles non linéaires, d'évolution, ou bien stationnaires. À titre d'exemple, cette méthode est appliquée à l'équation des milieux poreux, pour laquelle nous obtenons de nouvelles contractions. Cette méthode ouvre de nouvelles voies de recherche à explorer.

In this Note, we present a general and fairly simple method to design families of contractions for nonlinear partial differential equations, either of evolution type, or of stationary type. As a particular example, we apply this method to the porous medium equation, for which we get new contractions. This method opens new directions to explore.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2014.08.020
Monneau, Régis 1

1 CERMICS, École des ponts ParisTech, Université Paris-Est, 6 et 8, avenue Blaise-Pascal, Cité Descartes, Champs-sur-Marne, 77455 Marne-la-Vallée cedex 2, France 
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Monneau, Régis. The method of differential contractions. Comptes Rendus. Mathématique, Tome 353 (2015) no. 2, pp. 143-147. doi : 10.1016/j.crma.2014.08.020. http://archive.numdam.org/articles/10.1016/j.crma.2014.08.020/

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