Variational principle for weighted porous media equation

Alexandra Antoniouk (1) , Marc Arnaudon (2)

1 Dep. Nonlinear Analysis Institute of Mathematics NAS Ukraine
2 IMB - Institut de Mathématiques de Bordeaux

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.

Mots clés: variational principle; porous medium; incompressible fluid; diffusion flow

Domaines: Probabilités [math.PR]

Alexandra Antoniouk, Marc Arnaudon. Variational principle for weighted porous media equation. Comptes rendus de l'Académie des sciences. Série I, Mathématique, 2014, 352, pp.3463-3479. ⟨hal-00872159⟩