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Sibirskii Zhurnal Industrial'noi Matematiki, 2024, Volume 27, Number 3, Pages 143–156
DOI: https://doi.org/10.33048/SIBJIM.2024.27.310 (Mi sjim1295) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Inverse problems of finding a source in the heat equation from a nonlocal observation

K. B. Sabitovab

a Sterlitamak Branch of Ufa University of Science and Technology, Sterlitamak, Bashkortostan, 453103 Russia
b Mavlyutov Institute of Mechanics, Ufa Federal Research Center, Russian Academy of Sciences, Ufa, 450054 Russia
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DOI: https://doi.org/10.33048/SIBJIM.2024.27.310
Abstract: The article presents the statement of inverse problems of finding the right-hand side of the heat equation from an additional integral condition and justifies their Hadamard wellposedness in the class of regular solutions. The uniqueness of solutions of the problems is proved on the basis of integral identities. The solutions of the problems are constructed explicitly using separation of variables and the integral equation method.
Keywords: heat equation, inverse problem, uniqueness of solution, method of integral identities, existence of solution, series, integral equation, stability of solution.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 123021200015-5 (FMRS-2023-00-15)
This work was financially supported by the budgets of the Mavlyutov Institute of Mechanics of the Ufa Federal Research Center of the Russian Academy of Sciences, project no. 123021200015-5 (FMRS-2023-00-15)), and the Sterlitamak branch of the Ufa University of Science and Technology. No additional grants to carry out or direct this particular research were obtained.
Received: 27.11.2023
Revised: 27.03.2024
Accepted: 17.04.2024
English version:
Journal of Applied and Industrial Mathematics, 2024, Volume 18, Issue 3, Pages 536–547
DOI: https://doi.org/10.1134/S1990478924030141
Document Type: Article
UDC: 517.956
Language: Russian
Citation: K. B. Sabitov, “Inverse problems of finding a source in the heat equation from a nonlocal observation”, Sib. Zh. Ind. Mat., 27:3 (2024), 143–156; J. Appl. Industr. Math., 18:3 (2024), 536–547
Citation in format AMSBIB
\Bibitem{Sab24}
\by K.~B.~Sabitov
\paper Inverse problems of finding a source in the heat equation from a nonlocal observation
\jour Sib. Zh. Ind. Mat.
\yr 2024
\vol 27
\issue 3
\pages 143--156
\mathnet{http://mi.mathnet.ru/sjim1295}
\transl
\jour J. Appl. Industr. Math.
\yr 2024
\vol 18
\issue 3
\pages 536--547
\crossref{https://doi.org/10.1134/S1990478924030141}
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    • This publication is cited in the following 1 articles:
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