无界域上一类随机反应扩散方程不变测度的存在唯一性

Existence and Uniqueness of Invariant Measures for a Class of Stochastic Reaction-Diffusion Equations on Unbounded Domains

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L_(p)^(2)(R_(+)^(d))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.

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 e 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.