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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2013, Volume 53, Number 11, Pages 1784–1790
DOI: https://doi.org/10.7868/S0044466913110033
(Mi zvmmf9941)
 

This article is cited in 4 scientific papers (total in 4 papers)

Inverse problem for the diffusion equation in the case of spherical symmetry

A. M. Denisov, S. I. Solov'eva

Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119992, Russia
Full-text PDF (178 kB) Citations (4)
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Abstract: The initial boundary value problem for the diffusion equation is considered in the case of spherical symmetry and an unknown initial condition. Additional information used for determining the unknown initial condition is an external volume potential whose density is the Laplace operator applied to the solution of the initial boundary value problem. The uniqueness of the solution of the inverse problem is studied depending on the parameters entering into the boundary conditions. It is shown that the solution of the inverse problem is either unique or not unique up to a one-dimensional linear subspace.
Key words: diffusion equation, spherical symmetry, unknown initial condition, inverse problem, Sturm-Liouville problem, existence and uniqueness of solution.
Received: 22.05.2013
English version:
Computational Mathematics and Mathematical Physics, 2013, Volume 52, Issue 11, Pages 1607–1613
DOI: https://doi.org/10.1134/S0965542513110031
Bibliographic databases:
Document Type: Article
UDC: 519.633.9
Language: Russian
Citation: A. M. Denisov, S. I. Solov'eva, “Inverse problem for the diffusion equation in the case of spherical symmetry”, Zh. Vychisl. Mat. Mat. Fiz., 53:11 (2013), 1784–1790; Comput. Math. Math. Phys., 52:11 (2013), 1607–1613
Citation in format AMSBIB
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  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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    References:58
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