Ergodicity for Stochastic Porous Media Equations

Konstantinos Dareiotis, Benjamin Gess, Pavlos Tsatsoulis

Published 2019-07-10Version 1

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.