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Sibirskii Matematicheskii Zhurnal, 2012, Volume 53, Number 1, Pages 180–186
(Mi smj2297)
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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
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
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
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https://www.mathnet.ru/eng/smj2297 https://www.mathnet.ru/eng/smj/v53/i1/p180
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