{"title":"Averaging principle for slow-fast SPDEs driven by mixed noises","authors":"Haoyuan Li, Hongjun Gao, Shiduo Qu","doi":"10.1016/j.jde.2025.02.080","DOIUrl":null,"url":null,"abstract":"<div><div>This paper investigates a class of slow-fast stochastic partial differential equations driven by fractional Brownian motion and standard Brownian motion. Firstly, the well-posedness for such equations are established. Secondly, we provide the uniform <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>-estimation for slow variable relying on the mild stochastic sewing Lemma. Finally, we obtain the approximate solution for slow variable via averaging principle.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"430 ","pages":"Article 113209"},"PeriodicalIF":2.4000,"publicationDate":"2025-03-06","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/S0022039625002086","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
This paper investigates a class of slow-fast stochastic partial differential equations driven by fractional Brownian motion and standard Brownian motion. Firstly, the well-posedness for such equations are established. Secondly, we provide the uniform -estimation for slow variable relying on the mild stochastic sewing Lemma. Finally, we obtain the approximate solution for slow variable via averaging principle.
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
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