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

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

2010-10-04

arxiv.org/abs/1010.0551v1

Mathematics

Probability

Scientific paper

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.

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