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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2023, Volume 63, Number 7, Pages 1145–1155
DOI: https://doi.org/10.31857/S0044466923070141 (Mi zvmmf11586) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Partial Differential Equations

Inverse problems for the Helmholtz equation on finding the right-hand side with nonlocal integral observation

K. B. Sabitovab

a Institute of Mathematics with Computing Center, Ural Federal Research Center, Russian Academy of Sciences, 450008, Ufa, Russia
b Sterlitamak Branch, Ufa University of Science and Technology, 453103, Sterlitamak, Russia
Citations (1)
DOI: https://doi.org/10.31857/S0044466923070141
Abstract: The paper presents formulations of inverse problems for the Helmholtz equation on finding its right-hand side with a Samarskii–Ionkin-type additional integral condition and the justification of their well-posedness in the Hadamard sense in the class of regular solutions. The uniqueness of solutions of the formulated problems is proved on the basis of integral identities. Solutions of the problem are found in explicit form by the methods of separation of variables and integral equations.
Key words: elliptic equation, inverse problems, integral condition, method of integral identities, uniqueness, existence, series, integral equation, stability.
Received: 07.01.2023
Revised: 25.02.2023
Accepted: 30.03.2023
English version:
Computational Mathematics and Mathematical Physics, 2023, Volume 63, Issue 7, Pages 1254–1263
DOI: https://doi.org/10.1134/S0965542523070138
Bibliographic databases:
Document Type: Article
UDC: 517.956
Language: Russian
Citation: K. B. Sabitov, “Inverse problems for the Helmholtz equation on finding the right-hand side with nonlocal integral observation”, Zh. Vychisl. Mat. Mat. Fiz., 63:7 (2023), 1145–1155; Comput. Math. Math. Phys., 63:7 (2023), 1254–1263
Citation in format AMSBIB
\Bibitem{Sab23}
\by K.~B.~Sabitov
\paper Inverse problems for the Helmholtz equation on finding the right-hand side with nonlocal integral observation
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2023
\vol 63
\issue 7
\pages 1145--1155
\mathnet{http://mi.mathnet.ru/zvmmf11586}
\crossref{https://doi.org/10.31857/S0044466923070141}
\elib{https://elibrary.ru/item.asp?id=54238536}
\transl
\jour Comput. Math. Math. Phys.
\yr 2023
\vol 63
\issue 7
\pages 1254--1263
\crossref{https://doi.org/10.1134/S0965542523070138}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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