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Criteria of the Uniqueness of Solutions and Well-Posedness of Inverse Source Problems

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Abstract

In this paper, we study the relation between the well-posedness of the inverse problem of the recovering the source in an abstract differential equation and the basis property of a certain class of function systems in a Hilbert space. As a consequence, based on the results concerning the well-posedness of inverse problems, we obtain the Riesz basis property and—under certain additional conditions—the Bari basis property of such systems.

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  1. National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Moscow, Russia

    A. B. Kostin

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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya Tematicheskie Obzory, Vol. 133, Functional Analysis, 2017.

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Kostin, A.B. Criteria of the Uniqueness of Solutions and Well-Posedness of Inverse Source Problems. J Math Sci 230, 907–949 (2018). https://doi.org/10.1007/s10958-018-3799-8

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