Convergence to SPDEs for second order evolutionary equation with singular short–range correlated potential

IF 2.4 2区 数学 Q1 MATHEMATICS
Dong Su , Wei Wang
{"title":"Convergence to SPDEs for second order evolutionary equation with singular short–range correlated potential","authors":"Dong Su ,&nbsp;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.
二阶奇异短程相关势演化方程的SPDEs收敛性
导出了具有奇异短程相关势的二阶进化方程的随机均匀化问题。与一阶进化方程相比,由于二阶进化方程的非对称半群,在解的矩估计方面需要克服更多的困难。在我们的方法中,解是用Duhamel公式表示的,解的矩估计是用一些解析方法得到的。然后通过图解展开和混沌展开,证明了在空间白噪声的驱动下,解在分布上收敛于随机偏微分方程(SPDEs)的Stratonovich形式的解。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
CiteScore
4.40
自引率
8.30%
发文量
543
审稿时长
9 months
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
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:604180095
Book学术官方微信