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Vestnik Yuzhno-Ural'skogo Universiteta. Seriya Matematicheskoe Modelirovanie i Programmirovanie, 2015, Volume 8, Issue 4, Pages 131–137
DOI: https://doi.org/10.14529/mmp150413
(Mi vyuru296)
 

Short Notes

Research of mathematical model of inhomogeneous media the heating process

A. N. Naimov

Vologda State University, Vologda, Russian Federation
References:
Abstract: In the paper mathematical model of inhomogeneous medium "TEN–sand–air" heating is investigated. This model is used in engineering problems to calculate the temperature and thermal characteristics during heating. The methodology of these calculations was developed in works of academician A. N. Tikhonov and A. A. Samarskiy. The considered mathematical model is an initial-boundary value problem for heat equation on a finite interval. Our problem, in contrast to the classical problems, includes three unknowns: one unknown function of two variables in the equation and two unknown functions of a single variable in the boundary conditions. The solution of initial-boundary value problem is found in the form of series of functions. These series are constructed by solving of the corresponding boundary value Sturm–Liouville problem in the Kneser's form. It is proved that the series of functions constructed in this way determines a unique classical solution of the initial-boundary value problem. Uniqueness of solution is proved by energy inequalities method.
Keywords: the mathematical model of heat inhomogeneous medium; solution of initial-boundary value problem; method of energy inequalities.
Funding agency Grant number
Russian Foundation for Basic Research 15-01-04713a
Received: 03.04.2015
Bibliographic databases:
Document Type: Article
UDC: 517.4+958
MSC: 39A14, 39A60
Language: Russian
Citation: A. N. Naimov, “Research of mathematical model of inhomogeneous media the heating process”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 8:4 (2015), 131–137
Citation in format AMSBIB
\Bibitem{Nai15}
\by A.~N.~Naimov
\paper Research of mathematical model of inhomogeneous media the heating process
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2015
\vol 8
\issue 4
\pages 131--137
\mathnet{http://mi.mathnet.ru/vyuru296}
\crossref{https://doi.org/10.14529/mmp150413}
\elib{https://elibrary.ru/item.asp?id=24989390}
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