Invariant Measures of Stochastic Lattice Plate Equations: Stability, Ergodicity and Mixing

Abstract

This article is concerned with the stability, ergodicity and mixing of invariant measures of a class of stochastic lattice plate equations with nonlinear damping driven by a family of nonlinear white noise. The polynomial growth drift term has an arbitrary order growth rate, and the diffusion term is a family of locally Lipschitz continuous functions. By modifying and improving several energy estimates of the solutions uniformly for initial data when time is large enough, we prove that the noise intensity union of all invariant measures of the stochastic equation is tight on \(\ell ^2\times \ell ^2\) . Then, we show that the weak limit of every sequence of invariant measures in this union must be an invariant measure of the corresponding limiting equation under the locally Lipschitz assumptions on the drift and diffusion terms. Under some globally Lipschitz conditions on the drift and diffusion terms, we also prove that every invariant measure of the stochastic equation must be ergodic and exponentially mixing in the pointwise and Wasserstein metric sense.