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Matematicheskie Trudy, 2016, Volume 19, Number 1, Pages 178–198
DOI: https://doi.org/10.17377/mattrudy.2016.19.106 (Mi mt303) 		 
This article is cited in 3 scientific papers (total in 3 papers)

On some classes of inverse problems of recovering a source function

S. G. Pyatkovab, E. I. Safonovb

a Sobolev Institute of Mathematics, Novosibirsk, Russia
b Yugra State University, Khanty-Mansiisk, Russia
Full-text PDF (276 kB) Citations (3)
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DOI: https://doi.org/10.17377/mattrudy.2016.19.106
Abstract: In the article we examine the question on solvability, uniqueness, and some qualitative properties of solutions to inverse problems of recovering point sources (the right-hand sides of a special form) in a one-dimensional parabolic equation. The values of a solution at some collection of points are taken as the overdetermination conditions. Examples are exposed that show that the uniqueness fails without additional conditions on the mutual disposition of sources and measurement points.
Key words: second order parabolic equation, inverse problem, initial-boundary value problem, well-posedness, unconditional solvability, existence, uniqueness.
Funding agency Grant number
Russian Foundation for Basic Research 15-41-00063_р_урал_a
Received: 04.01.2016
English version:
Siberian Advances in Mathematics, 2017, Volume 27, Issue 2, Pages 119–132
DOI: https://doi.org/10.3103/S1055134417020031
Bibliographic databases:
Document Type: Article
UDC: 517.95
Language: Russian
Citation: S. G. Pyatkov, E. I. Safonov, “On some classes of inverse problems of recovering a source function”, Mat. Tr., 19:1 (2016), 178–198; Siberian Adv. Math., 27:2 (2017), 119–132
Citation in format AMSBIB
\Bibitem{PyaSaf16}
\by S.~G.~Pyatkov, E.~I.~Safonov
\paper On some classes of inverse problems of recovering a source function
\jour Mat. Tr.
\yr 2016
\vol 19
\issue 1
\pages 178--198
\mathnet{http://mi.mathnet.ru/mt303}
\crossref{https://doi.org/10.17377/mattrudy.2016.19.106}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3588302}
\elib{https://elibrary.ru/item.asp?id=25963588}
\transl
\jour Siberian Adv. Math.
\yr 2017
\vol 27
\issue 2
\pages 119--132
\crossref{https://doi.org/10.3103/S1055134417020031}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85019982847}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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