Comptes Rendus
no. 2
Partial differential equations
The method of differential contractions

Presented by: the Editorial Board

Régis Monneau1
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, Volume 353 (2015) no. 2, pp. 143-147.

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.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2014.08.020

Régis Monneau 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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Régis Monneau. The method of differential contractions. Comptes Rendus. Mathématique, Volume 353 (2015) no. 2, pp. 143-147. doi : 10.1016/j.crma.2014.08.020. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.08.020/

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