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, 2019, Volume 162, Pages 34–41 (Mi into439)  
Determining temperature fields in a spatially inhomogeneous nonlinear medium

A. V. Zhibera, N. M. Tsirelmanb

a Institute of Mathematics with Computing Centre — Subdivision of the Ufa Federal Research Centre of the Russian Academy of Sciences, Ufa
b Ufa State Aviation Technical University
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Abstract: A method of determining temperature fields in a spatially inhomogeneous medium with temperature-dependent thermophysical properties of the material is shown. For this purpose, point and nonlocal transformations of the nonstationary heat conduction equation are used. Examples of applying the theory for various boundary conditions in the spherical symmetric case are given.
Keywords: inhomogeneity, nonlinearity, spherical symmetry, point and nonlocal transformations, hollow ball, boundary conditions.
English version:
Journal of Mathematical Sciences (New York), 2021, Volume 257, Issue 3, Pages 305–312
DOI: https://doi.org/10.1007/s10958-021-05484-2
Bibliographic databases:
Document Type: Article
UDC: 536.2:517.9
MSC: 35Q51, 37K60
Language: Russian
Citation: A. V. Zhiber, N. M. Tsirelman, “Determining temperature fields in a spatially inhomogeneous nonlinear medium”, Complex Analysis. Mathematical Physics, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 162, VINITI, Moscow, 2019, 34–41; J. Math. Sci. (N. Y.), 257:3 (2021), 305–312
Citation in format AMSBIB
\Bibitem{ZhiTsi19}
\by A.~V.~Zhiber, N.~M.~Tsirelman
\paper Determining temperature fields in a spatially inhomogeneous nonlinear medium
\inbook Complex Analysis. Mathematical Physics
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2019
\vol 162
\pages 34--41
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into439}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=3981815}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2021
\vol 257
\issue 3
\pages 305--312
\crossref{https://doi.org/10.1007/s10958-021-05484-2}
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