{"title":"脉冲导数随时间变化的源的定位和密度测定","authors":"M. Idemen, A. Alkumru","doi":"10.1109/URSIGASS.2011.6050372","DOIUrl":null,"url":null,"abstract":"In this study an inverse source problem related to the source density f<inf>0</inf> (x) which is a function of bounded support and taking place in the wave equation Δu(x, t) − (1/c<sup>2</sup>) ∂<sup>2</sup> u(x, t) / ∂t<sup>2</sup> = − f<inf>0</inf> (x)δ'(t) is considered. An explicit expression of the solution is given in terms of the surface integral of the data which is measured on the boundary S of a convex domain D during certain finite time interval [0, T]. An illustrative example shows the applicability as well as the effectiveness of the method.","PeriodicalId":325870,"journal":{"name":"2011 XXXth URSI General Assembly and Scientific Symposium","volume":"33 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2011-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Location and density determination for a source with impulse derivative time variation\",\"authors\":\"M. Idemen, A. Alkumru\",\"doi\":\"10.1109/URSIGASS.2011.6050372\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this study an inverse source problem related to the source density f<inf>0</inf> (x) which is a function of bounded support and taking place in the wave equation Δu(x, t) − (1/c<sup>2</sup>) ∂<sup>2</sup> u(x, t) / ∂t<sup>2</sup> = − f<inf>0</inf> (x)δ'(t) is considered. An explicit expression of the solution is given in terms of the surface integral of the data which is measured on the boundary S of a convex domain D during certain finite time interval [0, T]. An illustrative example shows the applicability as well as the effectiveness of the method.\",\"PeriodicalId\":325870,\"journal\":{\"name\":\"2011 XXXth URSI General Assembly and Scientific Symposium\",\"volume\":\"33 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2011-10-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2011 XXXth URSI General Assembly and Scientific Symposium\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/URSIGASS.2011.6050372\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2011 XXXth URSI General Assembly and Scientific Symposium","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/URSIGASS.2011.6050372","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Location and density determination for a source with impulse derivative time variation
In this study an inverse source problem related to the source density f0 (x) which is a function of bounded support and taking place in the wave equation Δu(x, t) − (1/c2) ∂2 u(x, t) / ∂t2 = − f0 (x)δ'(t) is considered. An explicit expression of the solution is given in terms of the surface integral of the data which is measured on the boundary S of a convex domain D during certain finite time interval [0, T]. An illustrative example shows the applicability as well as the effectiveness of the method.
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