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, 2025, Volume 239, Pages 53–61
DOI: https://doi.org/10.36535/2782-4438-2025-239-53-61 (Mi into1338) 		 
Initial-boundary-value problems for some nonlinear mixed heat conductivity operators

V. N. Khankhasaev, S. I. Munyaev

East Suberia State University of Technology and Management, Ulan-Ude
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DOI: https://doi.org/10.36535/2782-4438-2025-239-53-61
Abstract: In this paper, we consider a computational model for a mixed nonlinear heat equation with boundary conditions of the third kind that describes the process of switching off an electric arc including the interval of its stable combustion until the moment of switching off and replacing the strictly hyperbolic heat equation with a hyperbolic-parabolic equation. The numerical simulation of this problem based on an implicit difference scheme and the heat balance method was performed by using the MathCad-15 software. Also, we prove the well-posedness of the first boundary-value problem for some high-order nonlinear equation.
Keywords: hyperbolic heat equation, nonlinear equation of mixed type, implicit difference scheme, third boundary condition, heat balance method, high order equations
Funding agency Grant number
Russian Science Foundation 23-21-00269
This work was supported by the Russian Science Foundation (project No. 23-21-00269).
English version:
Journal of Mathematical Sciences (New York), 2025, Volume 292, Issue 3, Pages 383–391
DOI: https://doi.org/10.1007/s10958-025-07923-w
Document Type: Article
UDC: 517.95; 532.5
MSC: 65M06, 80-10
Language: Russian
Citation: V. N. Khankhasaev, S. I. Munyaev, “Initial-boundary-value problems for some nonlinear mixed heat conductivity operators”, Proceedings of the 6th International Conference "Dynamic Systems and Computer Science: Theory and Applications" (DYSC 2024). Irkutsk, September 16-20, 2024. Part 2, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 239, VINITI, Moscow, 2025, 53–61; J. Math. Sci. (N. Y.), 292:3 (2025), 383–391
Citation in format AMSBIB
\Bibitem{KhaMun25}
\by V.~N.~Khankhasaev, S.~I.~Munyaev
\paper Initial-boundary-value problems for some nonlinear mixed heat conductivity operators
\inbook Proceedings of the 6th International Conference "Dynamic Systems and Computer Science: Theory and Applications" (DYSC 2024). Irkutsk, September 16-20, 2024. Part 2
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2025
\vol 239
\pages 53--61
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into1338}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2025
\vol 292
\issue 3
\pages 383--391
\crossref{https://doi.org/10.1007/s10958-025-07923-w}
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