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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2020, Volume 60, Number 9, Pages 1604–1619
DOI: https://doi.org/10.31857/S0044466920090148 (Mi zvmmf11137) 		 
Determination of compactly supported sources for the one-dimensional heat equation

V. V. Solov'ev

National Research Nuclear University "MEPhI", Moscow, 115409 Russia
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DOI: https://doi.org/10.31857/S0044466920090148
Abstract: The inverse problem of determining a source in the one-dimensional heat equation in the case of a Dirichlet boundary value problem is investigated. The trace of the solution of the direct problem on straight-line segments inside the domain at the final time is specified as overdetermination (i.e., additional information on the solution of the direct problem). A Fredholm alternative theorem for this problem is proved, and sufficient conditions for its unique solvability are obtained. The inverse problem is considered in classes of smooth functions with derivatives satisfying the Hölder condition.
Key words: heat equation, unknown source, inverse problem, uniqueness of solution, existence of solution.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 02.а03.21.0005
This work was supported by the Competitiveness Enhancement Program for the National Research Nuclear University “MEPhI” (Moscow Engineering Physics Institute), project no. 02.a03.21.0005 of August 27, 2013.
Received: 10.05.2019
Revised: 03.02.2020
Accepted: 09.04.2020
English version:
Computational Mathematics and Mathematical Physics, 2020, Volume 60, Issue 9, Pages 1555–1569
DOI: https://doi.org/10.1134/S0965542520090146
Bibliographic databases:
Document Type: Article
UDC: 517.95
Language: Russian
Citation: V. V. Solov'ev, “Determination of compactly supported sources for the one-dimensional heat equation”, Zh. Vychisl. Mat. Mat. Fiz., 60:9 (2020), 1604–1619; Comput. Math. Math. Phys., 60:9 (2020), 1555–1569
Citation in format AMSBIB
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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