{"title":"Studies on invariant measures of fractional stochastic delay Ginzburg-Landau equations on R<sup>n</sup>.","authors":"Hong Lu, Linlin Wang, Mingji Zhang","doi":"10.3934/mbe.2024241","DOIUrl":null,"url":null,"abstract":"<p><p>This paper is concerned with invariant measures of fractional stochastic delay Ginzburg-Landau equations on the entire space $ \\mathbb{R}^n $. We first derive the uniform estimates and the mean-square uniform smallness of the tails of solutions in corresponding space. Then we deduce the weak compactness of a set of probability distributions of the solutions applying the Ascoli-Arzel$ \\grave{a} $. We finally prove the existence of invariant measures by applying Krylov-Bogolyubov's method.</p>","PeriodicalId":49870,"journal":{"name":"Mathematical Biosciences and Engineering","volume":"21 4","pages":"5456-5498"},"PeriodicalIF":2.6000,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Biosciences and Engineering","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.3934/mbe.2024241","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
Abstract
This paper is concerned with invariant measures of fractional stochastic delay Ginzburg-Landau equations on the entire space $ \mathbb{R}^n $. We first derive the uniform estimates and the mean-square uniform smallness of the tails of solutions in corresponding space. Then we deduce the weak compactness of a set of probability distributions of the solutions applying the Ascoli-Arzel$ \grave{a} $. We finally prove the existence of invariant measures by applying Krylov-Bogolyubov's method.
期刊介绍:
Mathematical Biosciences and Engineering (MBE) is an interdisciplinary Open Access journal promoting cutting-edge research, technology transfer and knowledge translation about complex data and information processing.
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