English

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

Probability 2018-06-18 v1

Abstract

We prove new L2L^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 "ζ\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.

Keywords

Cite

@article{arxiv.1010.0551,
  title  = {The global random attractor for a class of stochastic porous media equations},
  author = {W. Beyn and B. Gess and P. Lescot and M. Röckner},
  journal= {arXiv preprint arXiv:1010.0551},
  year   = {2018}
}