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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 5 scientific papers (total in 5 papers)

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

M. O. Korpusovab, A. Yu. Perlovc, A. V. Tymoshenkod, R. S. Shafirea

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 (5)
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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
\Bibitem{KorPerTym23}
\by M.~O.~Korpusov, A.~Yu.~Perlov, A.~V.~Tymoshenko, R.~S.~Shafir
\paper On the Blow-Up of the Solution of a Nonlinear System of Equations of a Thermal-Electrical Model
\jour Mat. Zametki
\yr 2023
\vol 114
\issue 5
\pages 759--772
\mathnet{http://mi.mathnet.ru/mzm13956}
\crossref{https://doi.org/10.4213/mzm13956}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4716484}
\transl
\jour Math. Notes
\yr 2023
\vol 114
\issue 5
\pages 850--861
\crossref{https://doi.org/10.1134/S0001434623110202}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85187640352}
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  • https://doi.org/10.4213/mzm13956
  • https://www.mathnet.ru/eng/mzm/v114/i5/p759
    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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