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Teoreticheskaya i Matematicheskaya Fizika, 2024, Volume 219, Number 2, Pages 249–262
DOI: https://doi.org/10.4213/tmf10665 (Mi tmf10665) 		 
This article is cited in 3 scientific papers (total in 3 papers)

On the blow-up of the solution of a $(1+1)$-dimensional thermal–electrical model

M. V. Artemevaa, M. O. Korpusovab

a Faculty of Physics, Lomonosov Moscow State University, Moscow, Russia
b Peoples' Friendship University of Russia, Moscow, Russia
Full-text PDF (414 kB) First page Citations (3)
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DOI: https://doi.org/10.4213/tmf10665
Abstract: We consider a $(1+1)$-dimensional thermal–electrical model of semiconductor heating in an electric field. For the corresponding initial-boundary value problem, we prove the existence of a classical solution that cannot be continued in time and obtain sufficient conditions for the blow-up of the solution in a finite time.
Keywords: nonlinear Sobolev-type equations, solution blow-up, local solvability, nonlinear capacity, blow-up time estimates.
Funding agency Grant number
Russian Science Foundation 23-11-00056
This research was supported by the Russian Science Foundation under grant No. 23-11-00056.
Received: 26.12.2023
Revised: 26.12.2023
English version:
Theoretical and Mathematical Physics, 2024, Volume 219, Issue 2, Pages 748–760
DOI: https://doi.org/10.1134/S0040577924050040
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: M. V. Artemeva, M. O. Korpusov, “On the blow-up of the solution of a $(1+1)$-dimensional thermal–electrical model”, TMF, 219:2 (2024), 249–262; Theoret. and Math. Phys., 219:2 (2024), 748–760
Citation in format AMSBIB
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\paper On the~blow-up of the~solution of a~$(1+1)$-dimensional thermal--electrical model
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\vol 219
\issue 2
\pages 249--262
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\crossref{https://doi.org/10.4213/tmf10665}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4749817}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2024TMP...219..748A}
\transl
\jour Theoret. and Math. Phys.
\yr 2024
\vol 219
\issue 2
\pages 748--760
\crossref{https://doi.org/10.1134/S0040577924050040}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85194470107}
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  • https://doi.org/10.4213/tmf10665
  • https://www.mathnet.ru/eng/tmf/v219/i2/p249
    • This publication is cited in the following 3 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
    2. 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  mathnet  mathnet  crossref  crossref
    3. 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  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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