Ergodicity for Stochastic Porous Media Equations
- Authors: Konstantinos Dareiotis, Benjamin Gess, Pavlos Tsatsoulis
- Preprint year: 2019
- First public date: 2019-07-10
- arXiv: 1907.04605
- Status: Published
- Publication type: Journal article
- Publication year: 2020
- Journal: SIAM journal on mathematical analysis, 52 (2020) 5, pp. 4524-4564
- DOI: 10.1137/19M1278521
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.