Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2021, Volume 199, Pages 50–59
DOI: https://doi.org/10.36535/0233-6723-2021-199-50-59 (Mi into889) 		 
Application of generalized Bers degrees, the matrix method, and the Fourier method for solving the nonstationary heat equation in a multilayer medium

V. V. Kalmanovich, M. A. Stepovich

Tsiolkovsky Kaluga State University
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DOI: https://doi.org/10.36535/0233-6723-2021-199-50-59
Abstract: In this paper, we present an analytical method for solving the nonstationary heat equation in a multilayer medium without internal sources based on generalized Bers degrees, the matrix method, and the Fourier method. We propose an algorithm for solving this problem for various geometries of a multilayer medium (plane layers and layers with axial and central symmetry). Using this algorithm, we give examples for three-layer plane and axisymmetric structures.
Keywords: multilayer medium, matrix method, heat conduction problem, generalized Bers degree, Fourier method.
Funding agency Grant number
Russian Foundation for Basic Research 19-03-00271
18-41-400001
This work was supported by the Russian Foundation for Basic Research and the Government of the Kaluga Region (project Nos. 19-03-00271 and 18-41-400001).
Document Type: Article
UDC: 517.958
MSC: 35Q49
Language: Russian
Citation: V. V. Kalmanovich, M. A. Stepovich, “Application of generalized Bers degrees, the matrix method, and the Fourier method for solving the nonstationary heat equation in a multilayer medium”, Proceedings of the 20 International Saratov Winter School "Contemporary Problems of Function Theory and Their Applications", Saratov, January 28 — February 1, 2020. Part 1, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 199, VINITI, Moscow, 2021, 50–59
Citation in format AMSBIB
\Bibitem{KalSte21}
\by V.~V.~Kalmanovich, M.~A.~Stepovich
\paper Application of generalized Bers degrees, the matrix method, and the Fourier method for solving the nonstationary heat equation in a multilayer medium
\inbook Proceedings of the 20 International Saratov Winter School "Contemporary Problems of Function Theory and Their Applications", Saratov, January 28 --- February 1, 2020. Part 1
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2021
\vol 199
\pages 50--59
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into889}
\crossref{https://doi.org/10.36535/0233-6723-2021-199-50-59}
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