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Matematicheskie Zametki, 2022, Volume 112, Issue 3, Pages 398–411
DOI: https://doi.org/10.4213/mzm13472 (Mi mzm13472) 		 
This article is cited in 2 scientific papers (total in 2 papers)

The Inverse Problem of Recovering the Source Function in a Multidimensional Nonuniformly Parabolic Equation

V. L. Kamynin

National Engineering Physics Institute "MEPhI", Moscow
Full-text PDF (537 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm13472
Abstract: The unique solvability of the inverse problem of recovering the source function in a nonuniformly parabolic equation with many independent variables in a bounded domain is proved. As an additional condition, the integral observation condition is given. The unknown source function can be found by iteration from the operator equation with contraction operator. An example of an the inverse problem for which the results proved in this paper are applicable is presented. The results obtained for the inverse problem are based on the preliminary study of the unique solvability of the corresponding direct problem, which is also of interest in itself.
Keywords: the inverse problems, nonuniformly parabolic equations, integral observation.
Funding agency Grant number
Priority 2030 Program
This work was supported by the program “Priority-2030” of the National Research Nuclear University (MEPhI).
Received: 03.03.2022
English version:
Mathematical Notes, 2022, Volume 112, Issue 3, Pages 412–423
DOI: https://doi.org/10.1134/S0001434622090103
Bibliographic databases:
Document Type: Article
UDC: 517.95
Language: Russian
Citation: V. L. Kamynin, “The Inverse Problem of Recovering the Source Function in a Multidimensional Nonuniformly Parabolic Equation”, Mat. Zametki, 112:3 (2022), 398–411; Math. Notes, 112:3 (2022), 412–423
Citation in format AMSBIB
\Bibitem{Kam22}
\by V.~L.~Kamynin
\paper The Inverse Problem of Recovering the Source Function in a Multidimensional Nonuniformly Parabolic Equation
\jour Mat. Zametki
\yr 2022
\vol 112
\issue 3
\pages 398--411
\mathnet{http://mi.mathnet.ru/mzm13472}
\crossref{https://doi.org/10.4213/mzm13472}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4538777}
\transl
\jour Math. Notes
\yr 2022
\vol 112
\issue 3
\pages 412--423
\crossref{https://doi.org/10.1134/S0001434622090103}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85140333631}
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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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