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Teoreticheskaya i Matematicheskaya Fizika, 2023, Volume 217, Number 2, Pages 378–390
DOI: https://doi.org/10.4213/tmf10520
(Mi tmf10520)
 

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

Global-in-time solvability of a nonlinear system of equations of a thermal–electrical model with quadratic nonlinearity

M. O. Korpusovab, A. Yu. Perlovab, A. V. Tymoshenkoab, R. S. Shafirab

a Lomonosov Moscow State University, Faculty of Physics, Moscow, Russia
b Peoples' Friendship University of Russia, Moscow, Russia
Full-text PDF (412 kB) Citations (8)
References:
Abstract: A system of equations with a quadratic nonlinearity in the electric field potential and temperature is proposed to describe the process of heating of semiconductor elements of an electrical board, with the thermal and electrical “breakdowns” possible in the course of time. For this system of equations, the existence of a classical solution not extendable in time is proved and sufficient conditions for a unique global-in-time solvability are also obtained.
Keywords: nonlinear equations of Sobolev type, blow-up, local solubility, nonlinear capacity, estimates of blow-up time.
Funding agency Grant number
Russian Science Foundation 23-11-00056
This work was supported by the Russian Science Foundation (grant No. 23-11-00056).
Received: 16.04.2023
Revised: 25.05.2023
English version:
Theoretical and Mathematical Physics, 2023, Volume 217, Issue 2, Pages 1743–1754
DOI: https://doi.org/10.1134/S0040577923110090
Bibliographic databases:
Document Type: Article
MSC: 35Q
Language: Russian
Citation: 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”, TMF, 217:2 (2023), 378–390; Theoret. and Math. Phys., 217:2 (2023), 1743–1754
Citation in format AMSBIB
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\by M.~O.~Korpusov, A.~Yu.~Perlov, A.~V.~Tymoshenko, R.~S.~Shafir
\paper Global-in-time solvability of a~nonlinear system of equations of a~thermal--electrical model with quadratic nonlinearity
\jour TMF
\yr 2023
\vol 217
\issue 2
\pages 378--390
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\crossref{https://doi.org/10.4213/tmf10520}
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\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2023TMP...217.1743K}
\transl
\jour Theoret. and Math. Phys.
\yr 2023
\vol 217
\issue 2
\pages 1743--1754
\crossref{https://doi.org/10.1134/S0040577923110090}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85177655959}
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  • https://www.mathnet.ru/eng/tmf10520
  • https://doi.org/10.4213/tmf10520
  • https://www.mathnet.ru/eng/tmf/v217/i2/p378
  • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теоретическая и математическая физика Theoretical and Mathematical Physics
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    References:36
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