{"title":"A Stability Estimate in the Source Problem for the Radiative Transfer Equation","authors":"V. G. Romanov","doi":"10.1134/S106456242370134X","DOIUrl":null,"url":null,"abstract":"<p>A stability estimate for the solution of a source problem for the stationary radiative transfer equation is given. It is supposed that the source has an isotropic distribution. Earlier, stability estimates for this problem were found in a partial case of the emission tomography problem with a vanishing scattering operator and for the complete transfer equation under additional difficult-to-check conditions imposed on the absorption coefficient and the scattering kernel. In this work, we suggest a new fairly simple approach for obtaining a stability estimate for the problem under the consideration. The transfer equation is considered in a circle of the two-dimension space. In the forward problem, it is assumed that incoming radiation is absent. In the inverse problem of recovering the unknown source, data on solutions of the forward problem related to outgoing radiation are given on a portion of the boundary. The obtained result can be used to estimate the total density of distributed radiation sources.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-14","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/10.1134/S106456242370134X","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
A stability estimate for the solution of a source problem for the stationary radiative transfer equation is given. It is supposed that the source has an isotropic distribution. Earlier, stability estimates for this problem were found in a partial case of the emission tomography problem with a vanishing scattering operator and for the complete transfer equation under additional difficult-to-check conditions imposed on the absorption coefficient and the scattering kernel. In this work, we suggest a new fairly simple approach for obtaining a stability estimate for the problem under the consideration. The transfer equation is considered in a circle of the two-dimension space. In the forward problem, it is assumed that incoming radiation is absent. In the inverse problem of recovering the unknown source, data on solutions of the forward problem related to outgoing radiation are given on a portion of the boundary. The obtained result can be used to estimate the total density of distributed radiation sources.
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