Preprint of the project: SFB 701: Spectral Structures and Topological Methods in Mathematics - Project B3

Numerical Analysis of equivariant evolution equations

10-009 Wolf-Jürgen Beyn, Benjamin Gess, Paul Lescot, Michael Röckner.
The global random attractor for a class of stochastic porous media equations


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 "ζ-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.