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Sibirskii Matematicheskii Zhurnal, 2012, Volume 53, Number 1, Pages 180–186 (Mi smj2297)  

This article is cited in 86 scientific papers (total in 86 papers)

On a class of problems of determining the temperature and density of heat sources given initial and final temperature

I. Orazova, M. A. Sadybekovb

a M. O. Auezov South Kazakhstan State University, Shymkent, Kazakhstan
b Institute of Mathematics, Informatics and Mechanics, Almaty, Kazakhstan
References:
Abstract: We consider a class of problems modeling the process of determining the temperature and density of heat sources given initial and finite temperature. Their mathematical statements involve inverse problems for the heat equation in which, solving the equation, we have to find the unknown right-hand side depending only on the space variable. We prove the existence and uniqueness of classical solutions to the problem, solving the problem independently of whether the corresponding spectral problem (for the operator of multiple differentiation with not strongly regular boundary conditions) has a basis of generalized eigenfunctions.
Keywords: inverse problem, heat equation, initial temperature, final temperature, not strongly regular boundary conditions, Sturm-type boundary conditions, Fourier series, orthogonal basis.
Received: 02.02.2011
English version:
Siberian Mathematical Journal, 2012, Volume 53, Issue 1, Pages 146–151
DOI: https://doi.org/10.1134/S0037446612010120
Bibliographic databases:
Document Type: Article
UDC: 517.956.4
Language: Russian
Citation: I. Orazov, M. A. Sadybekov, “On a class of problems of determining the temperature and density of heat sources given initial and final temperature”, Sibirsk. Mat. Zh., 53:1 (2012), 180–186; Siberian Math. J., 53:1 (2012), 146–151
Citation in format AMSBIB
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\by I.~Orazov, M.~A.~Sadybekov
\paper On a~class of problems of determining the temperature and density of heat sources given initial and final temperature
\jour Sibirsk. Mat. Zh.
\yr 2012
\vol 53
\issue 1
\pages 180--186
\mathnet{http://mi.mathnet.ru/smj2297}
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\transl
\jour Siberian Math. J.
\yr 2012
\vol 53
\issue 1
\pages 146--151
\crossref{https://doi.org/10.1134/S0037446612010120}
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  • https://www.mathnet.ru/eng/smj/v53/i1/p180
  • This publication is cited in the following 86 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Сибирский математический журнал Siberian Mathematical Journal
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    References:83
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