Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2017, Volume 133, Pages 81–119 (Mi into191)  
This article is cited in 2 scientific papers (total 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
Full-text PDF (561 kB) Citations (2) English version article
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.
English version:
Journal of Mathematical Sciences (New York), 2018, Volume 230, Issue 6, Pages 907–949
DOI: https://doi.org/10.1007/s10958-018-3799-8
Bibliographic databases:
Document Type: Article
UDC: 517.95
MSC: 35P05, 35R30, 47F05
Language: Russian
Citation: A. B. Kostin, “Criteria of the uniqueness of solutions and well-posedness of inverse source problems”, Functional analysis, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 133, VINITI, Moscow, 2017, 81–119; J. Math. Sci. (N. Y.), 230:6 (2018), 907–949
Citation in format AMSBIB
\Bibitem{Kos17}
\by A.~B.~Kostin
\paper Criteria of the uniqueness of solutions and well-posedness of inverse source problems
\inbook Functional analysis
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2017
\vol 133
\pages 81--119
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into191}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=3799501}
\zmath{https://zbmath.org/?q=an:1391.35292}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2018
\vol 230
\issue 6
\pages 907--949
\crossref{https://doi.org/10.1007/s10958-018-3799-8}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85045058240}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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