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Teoreticheskaya i Matematicheskaya Fizika, 2025, Volume 222, Number 2, Pages 217–232
DOI: https://doi.org/10.4213/tmf10825 (Mi tmf10825) 		 
On the solvability of the Cauchy problem for a thermal–electrical model

M. V. Artemevaab, M. O. Korpusovab, A. A. Paninab

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/tmf10825
Abstract: We consider a thermal–electrical (3+1)-dimensional model of semiconductor heating in anЁelectric field. We prove the existence of a classical solution nonextendable in time for the corresponding Cauchy problem.
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 financially supported by the Russian Science Foundation (project No. 23-11-00056).
Received: 13.09.2024
Revised: 13.09.2024
English version:
Theoretical and Mathematical Physics, 2025, Volume 222, Issue 2, Pages 183–197
DOI: https://doi.org/10.1134/S0040577925020011
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: M. V. Artemeva, M. O. Korpusov, A. A. Panin, “On the solvability of the Cauchy problem for a thermal–electrical model”, TMF, 222:2 (2025), 217–232; Theoret. and Math. Phys., 222:2 (2025), 183–197
Citation in format AMSBIB
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\paper On the~solvability of the~Cauchy problem for a~ thermal--electrical model
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\vol 222
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\pages 217--232
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\jour Theoret. and Math. Phys.
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\pages 183--197
\crossref{https://doi.org/10.1134/S0040577925020011}
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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