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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2010, Issue 1(20), Pages 239–243 (Mi vsgtu745)  

Short Communication
Mathematical Modelling

Simulation of Heat Waves in An Nonlinear Anisotropic Space

V. F. Formalyov, I. A. Selin*, E. L. Kuznetcova

Dept. of Computational Mathematics and Programming, Moscow Aviation Institute (State University of Aerospace Technologies), Moscow

Abstract: For the first time analytical solution of the problem with boundary conditions in the non-linear anisotropic space for the quasilinear parabolic heat equation where heat conductivity tensor's components are temperature functions is obtained. This solution has show a wave type of the heat diffusion. Wave's fronts are ellipse in the anisotropic space at different time moment. Existence of the solution in wave's front and time derivative and space derivatives different orders has been analysed dependence from power of temperature which influences heat conductivity tensor's components.

Keywords: nonlinear problems, analytical methods, front of temperature indignation, additional boundary conditions, integral of thermal balance
* Author to whom correspondence should be addressed

DOI: https://doi.org/10.14498/vsgtu745

Full text: PDF file (351 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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Bibliographic databases:

UDC: 517.958+536.2(075)
MSC: 80A17, 80M25
Original article submitted 23/XI/2009
revision submitted – 10/XII/2009

Citation: V. F. Formalyov, I. A. Selin, E. L. Kuznetcova, “Simulation of Heat Waves in An Nonlinear Anisotropic Space”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 1(20) (2010), 239–243

Citation in format AMSBIB
\Bibitem{ForSelKuz10}
\by V.~F.~Formalyov, I.~A.~Selin, E.~L.~Kuznetcova
\paper Simulation of Heat Waves in An Nonlinear Anisotropic~Space
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2010
\vol 1(20)
\pages 239--243
\mathnet{http://mi.mathnet.ru/vsgtu745}
\crossref{https://doi.org/10.14498/vsgtu745}


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  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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