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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2011, Volume 51, Number 9, Pages 1695–1702 (Mi zvmmf9544)  
This article is cited in 2 scientific papers (total in 2 papers)

Inverse problem for the diffusion equation with overdetermination in the form of an external volume potential

A. M. Denisov

Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119992 Russia
Full-text PDF (544 kB) Citations (2)
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Abstract: An initial-boundary value problem for the diffusion equation with an unknown initial condition is considered. Additional information used for determining the unknown initial condition is an external volume potential whose density is the Laplacian calculated for the solution of the initial-boundary value problem. Uniqueness theorems for the inverse problem are proved in the case when the spatial domain of the initial-boundary value problem is a spherical layer or a parallelepiped.
Key words: diffusion equation, unknown initial condition, inverse problem, volume potential, eigenfunctions of Laplacian, uniqueness theorems.
Received: 18.03.2011
English version:
Computational Mathematics and Mathematical Physics, 2011, Volume 51, Issue 9, Pages 1588–1595
DOI: https://doi.org/10.1134/S0965542511090089
Bibliographic databases:
Document Type: Article
UDC: 519.633.9
Language: Russian
Citation: A. M. Denisov, “Inverse problem for the diffusion equation with overdetermination in the form of an external volume potential”, Zh. Vychisl. Mat. Mat. Fiz., 51:9 (2011), 1695–1702; Comput. Math. Math. Phys., 51:9 (2011), 1588–1595
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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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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    References:79
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