{"title":"Recovering initial states in semilinear parabolic problems from time-averages","authors":"Lina Sophie Schmitz, Christoph Walker","doi":"10.1016/j.jde.2025.02.049","DOIUrl":null,"url":null,"abstract":"<div><div>Well-posedness of certain semilinear parabolic problems with nonlocal initial conditions is shown in time-weighted spaces. The result is applied to recover the initial states in semilinear parabolic problems with nonlinearities of superlinear behavior near zero from small time-averages over arbitrary time periods.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"429 ","pages":"Pages 503-528"},"PeriodicalIF":2.4000,"publicationDate":"2025-02-21","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/S0022039625001688","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
Well-posedness of certain semilinear parabolic problems with nonlocal initial conditions is shown in time-weighted spaces. The result is applied to recover the initial states in semilinear parabolic problems with nonlinearities of superlinear behavior near zero from small time-averages over arbitrary time periods.
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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