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.

arXiv comment34 pages

References in corpus (5)

• Harnack inequality and applications for stochastic generalized porous media equations
• Random attractors for degenerate stochastic partial differential equations
• On L_p- theory for stochastic parabolic integro-differential equations
• Multi-valued, singular stochastic evolution inclusions
• Entropy solutions for stochastic porous media equations

Cited by in corpus (6)

• Porous media equations with multiplicative space-time white noise
• Numerical approximation of singular-degenerate parabolic stochastic PDEs
• Well-posedness of SVI solutions to singular-degenerate stochastic porous media equations arising in self-organised criticality
• Ergodicity for singular-degenerate porous media equations
• Synchronisation by noise for the stochastic quantisation equation in dimensions $2$ and $3$
• Ergodicity for stochastic conservation laws with multiplicative noise