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Well-posedness of a parabolic inverse problem

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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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Authors and Affiliations

  1. Department of Mathematics, Tianjin University, 300072, Tianjin, China

    Yu Wenhuan

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  1. Yu Wenhuan
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This research is partially supported by the National Natural Sciences Foundation of China.

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Yu, W. Well-posedness of a parabolic inverse problem. Acta Mathematicae Applicatae Sinica 13, 329–336 (1997). https://doi.org/10.1007/BF02025888

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  • DOI: https://doi.org/10.1007/BF02025888

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