Partial Differential Equations The method of differential contractions
نویسنده
چکیده
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. Résumé La méthode des contractions différentielles. Dans cette Note, nous présentons une méthode simple et générale pour fabriquer des familles de contractions pour des equations aux dérivées partielles non linéaires, d’évolution ou bien stationaires. A 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 directions de recherche à explorer.
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