Ergodicity for Stochastic Porous Media Equations

Abstract

The long time behaviour of solutions to stochastic porous media equations on smooth bounded domains with Dirichlet boundary data is studied. Based on weighted $L^1$-estimates the existence and uniqueness of invariant measures with optimal bounds on the rate of mixing are proved. Along the way the existence and uniqueness of entropy solutions is shown.

34 pages

References in corpus (1)

• Harnack inequality and applications for stochastic generalized porous media equations

Cited by in corpus (3)

• Numerical approximation of singular-degenerate parabolic stochastic PDEs
• Synchronisation by noise for the stochastic quantisation equation in dimensions $2$ and $3$
• Ergodicity for stochastic conservation laws with multiplicative noise