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arXiv · 1907.04605

Ergodicity for Stochastic Porous Media Equations

Konstantinos Dareiotis·Benjamin Gess·Pavlos Tsatsoulis
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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.

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Konstantinos Dareiotis, Benjamin Gess, Pavlos Tsatsoulis. 2019-07-10. Ergodicity for Stochastic Porous Media Equations. https://arxiv.org/abs/1907.04605

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