{"title":"Application of Rothe’s Method to a Parabolic Inverse Problem with Nonlocal Boundary Condition","authors":"Yong-Hyok Jo, Myong-Hwan Ri","doi":"10.21136/AM.2021.0029-21","DOIUrl":null,"url":null,"abstract":"<div><p>We consider an inverse problem for the determination of a purely time-dependent source in a semilinear parabolic equation with a nonlocal boundary condition. An approximation scheme for the solution together with the well-posedness of the problem with the initial value <i>u</i><sub>0</sub> ∈ <i>H</i><sup>1</sup>(Ω) is presented by means of the Rothe time-discretization method. Further approximation scheme via Rothe’s method is constructed for the problem when <i>u</i><sub>0</sub> ∈ <i>L</i><sup>2</sup>(Ω) and the integral kernel in the nonlocal boundary condition is symmetric.</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.21136/AM.2021.0029-21","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We consider an inverse problem for the determination of a purely time-dependent source in a semilinear parabolic equation with a nonlocal boundary condition. An approximation scheme for the solution together with the well-posedness of the problem with the initial value u0 ∈ H1(Ω) is presented by means of the Rothe time-discretization method. Further approximation scheme via Rothe’s method is constructed for the problem when u0 ∈ L2(Ω) and the integral kernel in the nonlocal boundary condition is symmetric.
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