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

TL;DR

This paper establishes the existence of global random attractors for a class of stochastic porous media equations, introducing new estimates and a novel notion of $\

Contribution

It introduces $\

Findings

Existence of global random attractors for stochastic porous media equations

The attractor reduces to a single random point in certain cases

New $L^2$-estimates and regularity results for these equations

Abstract

We prove new $L^2$-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 "$\zeta$-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.