SPD

Abstract

Joint work with Wolf-Jurgen Beyn, Benjamin Gess and Paul Lescot. 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 rst 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.