{"title":"辐射输运方程系数反问题的凸化数值解法","authors":"M. Klibanov, Jingzhi Li, L. Nguyen, Zhipeng Yang","doi":"10.1137/22m1509837","DOIUrl":null,"url":null,"abstract":". An ( n + 1) − D coefficient inverse problem for the radiative stationary transport equation is considered for the first time. A globally conver- gent so-called convexification numerical method is developed and its convergence analysis is provided. The analysis is based on a Carleman estimate. In particular, convergence analysis implies a certain uniqueness theorem. Exten-sive numerical studies in the 2-D case are presented. Our are the source along an interval of a line and the data are only at a part of the boundary of the of is unlike the classical case of X-ray tomography when the runs all around and the are on the","PeriodicalId":185319,"journal":{"name":"SIAM J. Imaging Sci.","volume":"20 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"Convexification Numerical Method for a Coefficient Inverse Problem for the Radiative Transport Equation\",\"authors\":\"M. Klibanov, Jingzhi Li, L. Nguyen, Zhipeng Yang\",\"doi\":\"10.1137/22m1509837\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". An ( n + 1) − D coefficient inverse problem for the radiative stationary transport equation is considered for the first time. A globally conver- gent so-called convexification numerical method is developed and its convergence analysis is provided. The analysis is based on a Carleman estimate. In particular, convergence analysis implies a certain uniqueness theorem. Exten-sive numerical studies in the 2-D case are presented. Our are the source along an interval of a line and the data are only at a part of the boundary of the of is unlike the classical case of X-ray tomography when the runs all around and the are on the\",\"PeriodicalId\":185319,\"journal\":{\"name\":\"SIAM J. Imaging Sci.\",\"volume\":\"20 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-01-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"SIAM J. Imaging Sci.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1137/22m1509837\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM J. Imaging Sci.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1137/22m1509837","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Convexification Numerical Method for a Coefficient Inverse Problem for the Radiative Transport Equation
. An ( n + 1) − D coefficient inverse problem for the radiative stationary transport equation is considered for the first time. A globally conver- gent so-called convexification numerical method is developed and its convergence analysis is provided. The analysis is based on a Carleman estimate. In particular, convergence analysis implies a certain uniqueness theorem. Exten-sive numerical studies in the 2-D case are presented. Our are the source along an interval of a line and the data are only at a part of the boundary of the of is unlike the classical case of X-ray tomography when the runs all around and the are on the
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