{"title":"Effective dynamics for a class of stochastic weakly damped wave equation with a fast oscillation","authors":"Jin-Wei Zhao, B. Ge, Lu Liu","doi":"10.1063/5.0137730","DOIUrl":null,"url":null,"abstract":"The purpose of this paper is to consider the effective dynamic behavior of a class of stochastic weakly damped wave equations with a fast oscillation under the non-Lipschitz condition. We show that the slow component converges to the solution of the corresponding average equation. The result presented here extends the existing results from the Lipschitz to non-Lipschitz condition, which is a much weaker condition with a wider range of applications.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"58 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Physics Analysis Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1063/5.0137730","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
The purpose of this paper is to consider the effective dynamic behavior of a class of stochastic weakly damped wave equations with a fast oscillation under the non-Lipschitz condition. We show that the slow component converges to the solution of the corresponding average equation. The result presented here extends the existing results from the Lipschitz to non-Lipschitz condition, which is a much weaker condition with a wider range of applications.
期刊介绍：
Journal of Mathematical Physics, Analysis, Geometry (JMPAG) publishes original papers and reviews on the main subjects:
mathematical problems of modern physics;
complex analysis and its applications;
asymptotic problems of differential equations;
spectral theory including inverse problems and their applications;
geometry in large and differential geometry;
functional analysis, theory of representations, and operator algebras including ergodic theory.
The Journal aims at a broad readership of actively involved in scientific research and/or teaching at all levels scientists.
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