{"title":"Convergence to SPDEs for second order evolutionary equation with singular short–range correlated potential","authors":"Dong Su , Wei Wang","doi":"10.1016/j.jde.2025.113497","DOIUrl":null,"url":null,"abstract":"<div><div>The random homogenization for second order evolutionary equation with singular short–range correlated potential is derived. Comparing with the first order evolutionary equation, more difficulty need to be overcome in the moment estimation of the solution due to non–symmetrical semigroup of second order evolutionary equation. In our approach the solution is written out by the Duhamel's formula and the moment estimation of the solution is obtained by some analytic methods. Then by means of diagrammatic expansions and chaos expansions, the solution is shown to converge in distribution to the solution of stochastic partial differential equations (SPDEs) in Stratonovich form driven by spatial white noise.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"442 ","pages":"Article 113497"},"PeriodicalIF":2.4000,"publicationDate":"2025-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022039625005248","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
The random homogenization for second order evolutionary equation with singular short–range correlated potential is derived. Comparing with the first order evolutionary equation, more difficulty need to be overcome in the moment estimation of the solution due to non–symmetrical semigroup of second order evolutionary equation. In our approach the solution is written out by the Duhamel's formula and the moment estimation of the solution is obtained by some analytic methods. Then by means of diagrammatic expansions and chaos expansions, the solution is shown to converge in distribution to the solution of stochastic partial differential equations (SPDEs) in Stratonovich form driven by spatial white noise.
期刊介绍:
The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools.
Research Areas Include:
• Mathematical control theory
• Ordinary differential equations
• Partial differential equations
• Stochastic differential equations
• Topological dynamics
• Related topics