{"title":"Invariant Measures of Stochastic Lattice Plate Equations: Stability, Ergodicity and Mixing","authors":"","doi":"10.1007/s40840-024-01685-5","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>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 <span> <span>\\(\\ell ^2\\times \\ell ^2\\)</span> </span>. 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.</p>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s40840-024-01685-5","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
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.
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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