SIAM Journal on Mathematical Analysis, Volume 52, Issue 5, Page 4524-4564, January 2020.
The long time behavior of solutions to stochastic porous media equations with nonlinear multiplicative noise on 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 are shown.

中文翻译：

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具有乘性噪声的随机多孔介质方程的遍历性

SIAM数学分析杂志，第52卷，第5期，第4524-4564页，2020年1月
。研究了具有Dirichlet边界数据的有界区域上具有非线性乘性噪声的随机多孔介质方程解的长时间行为。基于加权的$ L ^ {1} $估计，证明了在混合速率上具有最优边界的不变测度的存在性和唯一性。沿途显示了熵解的存在性和唯一性。