M. O. Korpusov, A. Yu. Perlov, A. V. Tymoshenko, R. S. Shafir, “On the Blow-Up of the Solution of a Nonlinear System of Equations of a Thermal-Electrical Model”, Mat. Zametki, 114:5 (2023), 759–772; Math. Notes, 114:5 (2023), 850

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Matematicheskie Zametki, 2023, Volume 114, Issue 5, Pages 759–772
DOI: https://doi.org/10.4213/mzm13956 (Mi mzm13956)

This article is cited in 8 scientific papers (total in 8 papers)

On the Blow-Up of the Solution of a Nonlinear System of Equations of a Thermal-Electrical Model

M. O. Korpusov^ab, A. Yu. Perlov^c, A. V. Tymoshenko^d, R. S. Shafir^ea

^a Peoples' Friendship University of Russia, Moscow
^b Faculty of Physics, Lomonosov Moscow State University
^c National Research University of Electronic Technology
^d Moscow Aviation Institute (National Research University)
^e Lomonosov Moscow State University

Full-text PDF (565 kB) Citations (8)

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DOI: https://doi.org/10.4213/mzm13956

Abstract: In this paper, we propose a system of nonlinear equations for the electric field potential and temperature, which describes the process of heating the semiconductor elements of an electrical board followed by thermal breakdown. For this system of equations, we prove the existence of a classical solution that is not extendable in time and also obtain sufficient conditions for the solution to blow up in finite time.

Keywords: electric field potential, first boundary value problem for the heat equation, Green's function, solution blow-up, methods of nonlinear capacity and test functions.

Funding agency	Grant number
Russian Science Foundation	23-11-00056
This work was financially supported by the Russian Science Foundation, project 23-11-00056, https://rscf.ru/en/project/23-11-00056/.

Received: 21.03.2023

English version:
Mathematical Notes, 2023, Volume 114, Issue 5, Pages 850–861
DOI: https://doi.org/10.1134/S0001434623110202

Bibliographic databases:

Document Type: Article

UDC: 517.957

MSC: 35K70

Language: Russian

Citation: M. O. Korpusov, A. Yu. Perlov, A. V. Tymoshenko, R. S. Shafir, “On the Blow-Up of the Solution of a Nonlinear System of Equations of a Thermal-Electrical Model”, Mat. Zametki, 114:5 (2023), 759–772; Math. Notes, 114:5 (2023), 850–861

Citation in format AMSBIB

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\paper On the Blow-Up of the Solution of a Nonlinear System of Equations of a Thermal-Electrical Model

\jour Mat. Zametki

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\issue 5

\pages 759--772

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\crossref{https://doi.org/10.4213/mzm13956}

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\jour Math. Notes

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\pages 850--861

\crossref{https://doi.org/10.1134/S0001434623110202}

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Linking options:

https://www.mathnet.ru/eng/mzm13956

https://doi.org/10.4213/mzm13956

https://www.mathnet.ru/eng/mzm/v114/i5/p759

This publication is cited in the following 8 articles:

M. V. Artemeva, M. O. Korpusov, A. A. Panin, “On the solvability of the Cauchy problem for a thermal–electrical model”, Theoret. and Math. Phys., 222:2 (2025), 183–197
M. V. Artemeva, M. O. Korpusov, “On the Existence of a Nonextendable Solution of the Cauchy problem for a $(1+1)$-Dimensional Thermal-Electrical Model”, Math. Notes, 115:5 (2024), 653–663
M. V. Artemeva, M. O. Korpusov, “On the blow-up of the solution of a $(1+1)$-dimensional thermal–electrical model”, Theoret. and Math. Phys., 219:2 (2024), 748–760
M. V Artemeva, M. O Korpusov, “THE CAUCHY PROBLEM FOR AN NONLINEAR WAVE EQUATION”, Differencialʹnye uravneniâ, 60:10 (2024), 1299
M. V. Artemeva, M. O. Korpusov, “On the existence of a nonextendable solution of the Cauchy problem for a $(3+1)$-dimensional thermal–electrical model”, Theoret. and Math. Phys., 221:3 (2024), 2207–2218
A. V. Timoshenko, A. Yu. Perlov, R. S. Shafir, A. N. Silenok, “Estimation of Reliability of a Radio-Electronic System with Uncertain Data on the Failure Rate of Its Components as a Result of Destructive Temperature Effects”, Russ. Aeronaut., 67:3 (2024), 718
M. V. Artemeva, M. O. Korpusov, “The Cauchy Problem for a Nonlinear Wave Equation”, Diff Equat, 60:10 (2024), 1369
M. O. Korpusov, A. Yu. Perlov, A. V. Tymoshenko, R. S. Shafir, “Global-in-time solvability of a nonlinear system of equations of a thermal–electrical model with quadratic nonlinearity”, Theoret. and Math. Phys., 217:2 (2023), 1743–1754

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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References:	44
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