Geodesic
Initial-boundary-value problems for some nonlinear mixed heat conductivity operators
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 6th International Conference "Dynamic Systems and Computer Science: Theory and Applications" (DYSC 2024). Irkutsk, September 16-20, 2024. Part 2, Tome 239 (2025), pp. 53-61

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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 
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     author = {V. N. Khankhasaev and S. I. Munyaev},
     title = {Initial-boundary-value problems for some nonlinear mixed heat conductivity operators},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
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V. N. Khankhasaev; S. I. Munyaev. Initial-boundary-value problems for some nonlinear mixed heat conductivity operators. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 6th International Conference "Dynamic Systems and Computer Science: Theory and Applications" (DYSC 2024). Irkutsk, September 16-20, 2024. Part 2, Tome 239 (2025), pp. 53-61. http://geodesic.mathdoc.fr/item/INTO_2025_239_a5/