| WELL-POSEDNESS OF A PARABOLIC INVERSE PROBLEM |
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| 作者姓名： | 喻文焕 |
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| 作者单位： | Department of Mathematics，Tianjin University，Tianjin 300072，China |
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| 摘 要： | 1.IntroductionItiswellknownthatinverseproblemsinpartialdifferentialequations,mostofwhichhavenotyetbeensolveduptonow,remainasachallengeinappliedmathematics.Therefore,manymathematiciansstudiedvariousinverseproblemsforparabolicequa-tions.FOrasimplesurveywereferto1,2,8,9]foridentifyingcoefficients,7]foridentifyingboundaryvalues,4,10]foridentifyingsourcetermsofparabolicequations.Wehavenotincludedalotofpapersconcerningthecomputationalmethodsusedforsolvinginverseparabolicproblems.Inthispaperthein…
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| 收稿时间： | 30 December 1993 |
Well-posedness of a parabolic inverse problem |
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| Wenhuan Yu.WELL-POSEDNESS OF A PARABOLIC INVERSE PROBLEM[J].Acta Mathematicae Applicatae Sinica,1997,13(3):329-336. |
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| Authors: | Wenhuan Yu |
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| Institution: | (1) Department of Mathematics, Tianjin University, 300072 Tianjin, China |
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| Abstract: | In this paper the inverse problem of determining the source term, which is independent of the time variable, of a linear, uniformly-parabolic equation is investigated. The uniqueness of the inverse problem is proved under mild assumptions by using the orthogonality method and an elimination method. The existence of the inverse problem is proved by means of the theory of solvable operators between Banach spaces; moreover, the continuous dependence on measurement of the solution to the inverse problem is also proved. |
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| Keywords: | Inverse problems for parabolic differential equations well-posedness uniqueness existence of inverse problems |
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