{"title":"A HOLDER STABILITY ESTIMATE FOR A COEFFICIENT ̈ INVERSE PROBLEM FOR THE WAVE EQUATION WITH A POINT SOURCE","authors":"M. Klibanov, V. Romanov","doi":"10.32523/2306-6172-2022-10-2-11-25","DOIUrl":null,"url":null,"abstract":"We consider a 3D coefficient inverse problem for the wave-like equation with backscattering non-overdetermined data. The forward problem is the Cauchy problem with the initial condition as the delta-function concentrated at a single location of the point source. We reduce the original problem to a problem with finite differences with respect to two out of three spatial variables and study an inverse problem for it. A stability estimate is stated for this reduced inverse problem.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.32523/2306-6172-2022-10-2-11-25","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
We consider a 3D coefficient inverse problem for the wave-like equation with backscattering non-overdetermined data. The forward problem is the Cauchy problem with the initial condition as the delta-function concentrated at a single location of the point source. We reduce the original problem to a problem with finite differences with respect to two out of three spatial variables and study an inverse problem for it. A stability estimate is stated for this reduced inverse problem.
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