This article is cited in 2 papers

Criteria of the uniqueness of solutions and well-posedness of inverse source problems

A. B. Kostin

National Engineering Physics Institute "MEPhI", Moscow

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

UDC: 517.95

MSC: 35P05, 35R30, 47F05

 English version: Journal of Mathematical Sciences (New York), 2018, 230:6, 907–949

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