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

W. Beyn; B. Gess; P. Lescot; M. Röckner

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arXiv · 1010.0551

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

W. Beyn·B. Gess·P. Lescot·M. Röckner

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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.

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BibTeX RIS

W. Beyn, B. Gess, P. Lescot, M. Röckner. 2010-10-04. The global random attractor for a class of stochastic porous media equations. https://arxiv.org/abs/1010.0551

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