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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2018, Volume 58, Number 5, Pages 778–789
DOI: https://doi.org/10.7868/S0044466918050083 (Mi zvmmf10736) 		 
This article is cited in 2 scientific papers (total in 2 papers)

On determining sources with compact supports in a bounded plane domain for the heat equation

V. V. Solov'ev

National Research Nuclear University “MEPhI”, Moscow, Russia
Citations (2)
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DOI: https://doi.org/10.7868/S0044466918050083
Abstract: The inverse problem of determining the source for the heat equation in a bounded domain on the plane is studied. The trace of the solution of the direct problem on two straight line segments inside the domain is given 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 whose derivatives satisfy 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
Received: 24.04.2017
English version:
Computational Mathematics and Mathematical Physics, 2018, Volume 58, Issue 5, Pages 750–760
DOI: https://doi.org/10.1134/S0965542518050159
Bibliographic databases:
Document Type: Article
UDC: 519.633
Language: Russian
Citation: V. V. Solov'ev, “On determining sources with compact supports in a bounded plane domain for the heat equation”, Zh. Vychisl. Mat. Mat. Fiz., 58:5 (2018), 778–789; Comput. Math. Math. Phys., 58:5 (2018), 750–760
Citation in format AMSBIB
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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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