无界域上一类随机反应扩散方程不变测度的存在唯一性

邓海斌　李晓军

摘要：研究定义在无界区域上的一类随机反应扩散方程不变测度的存在性和唯一性.利用方程主部算子在权空间L2ρ（Rd+）上生成算子半群的指数衰减性，对方程的解进行整体期望有界估计，并得到随机稳态解的存在性和指数稳定性，进而得到稳态解的分布为唯一的不变测度.

关键词：随机反应扩散方程; 不变测度; 指数稳定

中图分类号：O175.26 文献标志码：A 文章编号：1001-8395（2023）05-0608-08

1相关引理和概念

2稳态解的指数稳定性和一致有界性

3不变测度的存在唯一性

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Existence and Uniqueness of Invariant Measures for a Class of

Stochastic Reaction-Diffusion Equations on Unbounded DomainsDENG Haibin，LI Xiaojun（College of Science， Hohai University， Nanjing 211100， Jiangsu）

Abstract：In this paper， we study the existence and uniqueness of invariant measures for a class of stochastic reaction-diffusion equations defined on unbounded domains. Using the exponential decay of the operator semigroup generated by the linear operator of the equation on the weight space L2ρ（Rd+）， we get the global boundness of expectation estimation of solution， obtain the existence and exponential stability of the stochastic stationary solution， and deduce that the distribution of the stationary solution is the unique invariant measure.

Keywords：stochastic reaction-diffusion equations; invariant measure; exponential stability 〖=〗

2020 MSC：35K57; 60H15

（編辑 余毅）