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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2024, Volume 64, Number 3, Pages 443–461
DOI: https://doi.org/10.31857/S0044466924030062 (Mi zvmmf11717) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Partial Differential Equations

Uniqueness of a solution to the Lavrent’ev integral equation in $n$-dimensional space

M. M. Kokurin, V. V. Klyuchev, A. V. Gavrilova

Mari State University, 424001, Yoshkar-Ola, Republic of Mari El, Russia
Full-text PDF Citations (1)
DOI: https://doi.org/10.31857/S0044466924030062
Abstract: We study the multidimensional analogue of the Lavrent’ev integral equation to which an inverse problem of acoustic sounding is reduced. Conditions under which the studied equation has a unique solution are established. Results of numerical experiments concerning the solution of the inverse acoustic problem with variously located sets of sources and detectors are presented.
Key words: hyperbolic equation, coefficient inverse problem, inverse problem of acoustics, linear integral equation, Lavrent’ev equation, solution uniqueness, harmonic functions, complete system of functions, uniqueness set.
Funding agency Grant number
Russian Science Foundation 22-71-10070
This work was supported by the Russian Science Foundation, project no. 22-71-10070.
Received: 02.10.2023
Revised: 02.11.2023
Accepted: 17.11.2023
English version:
Computational Mathematics and Mathematical Physics, 2024, Volume 64, Issue 3, Pages 416–431
DOI: https://doi.org/10.1134/S0965542524030084
Bibliographic databases:
Document Type: Article
UDC: 517.935
Language: Russian
Citation: M. M. Kokurin, V. V. Klyuchev, A. V. Gavrilova, “Uniqueness of a solution to the Lavrent’ev integral equation in $n$-dimensional space”, Zh. Vychisl. Mat. Mat. Fiz., 64:3 (2024), 443–461; Comput. Math. Math. Phys., 64:3 (2024), 416–431
Citation in format AMSBIB
\Bibitem{KokKlyGav24}
\by M.~M.~Kokurin, V.~V.~Klyuchev, A.~V.~Gavrilova
\paper Uniqueness of a solution to the Lavrent’ev integral equation in $n$-dimensional space
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2024
\vol 64
\issue 3
\pages 443--461
\mathnet{http://mi.mathnet.ru/zvmmf11717}
\crossref{https://doi.org/10.31857/S0044466924030062}
\elib{https://elibrary.ru/item.asp?id=73160214}
\transl
\jour Comput. Math. Math. Phys.
\yr 2024
\vol 64
\issue 3
\pages 416--431
\crossref{https://doi.org/10.1134/S0965542524030084}
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  • https://www.mathnet.ru/eng/zvmmf/v64/i3/p443
    • This publication is cited in the following 1 articles:
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    		Æóðíàë âû÷èñëèòåëüíîé ìàòåìàòèêè è ìàòåìàòè÷åñêîé ôèçèêè Computational Mathematics and Mathematical Physics
     
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