Variational principle for weighted porous media equation

Authors :: Alexandra V. Antoniouk
Marc Arnaudon
Dep. Nonlinear Analysis Institute of Mathematics NAS Ukraine
Department of Nonlinear Analysis [Kyiv]
Institute of Mathematics of NAS of Ukraine
National Academy of Sciences of Ukraine (NASU)-National Academy of Sciences of Ukraine (NASU)-Institute of Mathematics of NAS of Ukraine
National Academy of Sciences of Ukraine (NASU)-National Academy of Sciences of Ukraine (NASU)
Institut de Mathématiques de Bordeaux (IMB)
Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)
Source :: Comptes rendus de l'Académie des sciences. Série I, Mathématique, Comptes rendus de l'Académie des sciences. Série I, Mathématique, Elsevier, 2014, 352, pp.3463-3479
Publication Year :: 2014
Publisher :: Elsevier BV, 2014.
Abstract: International audience; In this paper we state the variational principle for the weighted porous media equation. It extends V.I. Arnold's approach to the description of Euler flows as a geodesics on some manifold, i.e. as a critical points of some energy functional.

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