The global random attractor for a class of stochastic porous media equations

Paul Lescot (1) , Michael Roeckner (2) , Benjamin Gess (2) , Wolf-Jürgen Beyn (2)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem
2 SFB 701 - Fakultaet fuer Mathematik, SFB 701

We prove new L2-estimates and regularity results for generalized porous media equations "shifted by" a function-valued Wiener path. To include Wiener paths with merely first spatial (weak) derivates we introduce the notion of " -monotonicity" for the non-linear function in the equation. As a consequence we prove that stochastic porous media equations have global random attractors. In addition, we show that (in particular for the classical stochastic porous media equation) this attractor consists of a random point.

Domaines: Probabilités [math.PR]

Paul Lescot, Michael Roeckner, Benjamin Gess, Wolf-Jürgen Beyn. The global random attractor for a class of stochastic porous media equations. Comm. Partial Differential Equations, 2011, 36 (3), pp.446--469. ⟨hal-00877562⟩