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Journal of Mathematical Sciences

, Volume 230, Issue 6, pp 907–949 | Cite as

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

  • A. B. Kostin
Article
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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.

Keywords and phrases

inverse problem equation in Hilbert space final observation well-posedness completeness Riesz basis property 

AMS Subject Classification

35P05 35R30 47F05 

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Authors and Affiliations

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

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