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Teoreticheskaya i Matematicheskaya Fizika, 2024, Volume 221, Number 3, Pages 702–715
DOI: https://doi.org/10.4213/tmf10745 (Mi tmf10745) 		 
This article is cited in 1 scientific paper (total in 1 paper)

On the existence of a nonextendable solution of the Cauchy problem for a $(3+1)$-dimensional thermal–electrical model

M. V. Artemevaab, M. O. Korpusovab

a Faculty of Physics, Lomonosov Moscow State University, Moscow, Russia
b Peoples' Friendship University of Russia, Moscow, Russia
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DOI: https://doi.org/10.4213/tmf10745
Abstract: A thermal–electrical $(3+1)$-dimensional model of heating a semiconductor in an electric field is considered. For the corresponding Cauchy problem, the existence of a classical solution nonextendable in time is proved and an a priori estimate global in time is obtained.
Keywords: nonlinear Sobolev-type equations, local solvability, nonlinear capacity, blow-up time estimates.
Funding agency Grant number
Russian Science Foundation 23-11-00056
This work was carried out with the financial support of the Russian Science Foundation (project No. 23-11-00056).
Received: 26.04.2024
Revised: 27.08.2024
English version:
Theoretical and Mathematical Physics, 2024, Volume 221, Issue 3, Pages 2207–2218
DOI: https://doi.org/10.1134/S0040577924120146
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: 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”, TMF, 221:3 (2024), 702–715; Theoret. and Math. Phys., 221:3 (2024), 2207–2218
Citation in format AMSBIB
\Bibitem{ArtKor24}
\by M.~V.~Artemeva, M.~O.~Korpusov
\paper On the~existence of a~nonextendable solution of the~Cauchy problem for a~$(3+1)$-dimensional thermal--electrical model
\jour TMF
\yr 2024
\vol 221
\issue 3
\pages 702--715
\mathnet{http://mi.mathnet.ru/tmf10745}
\crossref{https://doi.org/10.4213/tmf10745}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2024TMP...221.2207A}
\transl
\jour Theoret. and Math. Phys.
\yr 2024
\vol 221
\issue 3
\pages 2207--2218
\crossref{https://doi.org/10.1134/S0040577924120146}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85212973811}
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  • https://doi.org/10.4213/tmf10745
  • https://www.mathnet.ru/eng/tmf/v221/i3/p702
    • This publication is cited in the following 1 articles:
    1. 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  mathnet  crossref  crossref  adsnasa
    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:15
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