no. 1
Partial differential equations/Probability theory
Variational principle for weighted porous media equation
[Principe variationnel pour lʼéquation des milieux poreux]

Présenté par : the Editorial Board

Antoniouk, Alexandra1 ; Arnaudon, Marc2
1 Department of Nonlinear Analysis, Institute of Mathematics NAS Ukraine, Tereschchenkivska str. 3, Kyiv 01 601, Ukraine
2 Institut de mathématiques de Bordeaux, CNRS UMR 5251, Université Bordeaux-1, 33405 Talence cedex, France
Comptes Rendus. Mathématique, Tome 352 (2014) no. 1, pp. 31-34.

Dans cette article, on établit un principe variationnel pour lʼéquation des milieux poreux. On généralise ainsi la description de V.I. Arnold des flots dʼEuler par des géodésiques vues comme des points critiques dʼune fonctionnelle dʼénergie.

In this paper we state the variational principle for the weighted porous media equation. It extends V.I. Arnoldʼs approach to the description of Euler flows as a geodesics on some manifold, i.e. as critical points of some energy functional.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2013.11.014
Antoniouk, Alexandra 1 ; Arnaudon, Marc 2

1 Department of Nonlinear Analysis, Institute of Mathematics NAS Ukraine, Tereschchenkivska str. 3, Kyiv 01 601, Ukraine
2 Institut de mathématiques de Bordeaux, CNRS UMR 5251, Université Bordeaux-1, 33405 Talence cedex, France 
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Antoniouk, Alexandra; Arnaudon, Marc. Variational principle for weighted porous media equation. Comptes Rendus. Mathématique, Tome 352 (2014) no. 1, pp. 31-34. doi : 10.1016/j.crma.2013.11.014. http://www.numdam.org/articles/10.1016/j.crma.2013.11.014/

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