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

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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. Korpusov^ab, A. Yu. Perlov^ab, A. V. Tymoshenko^ab, R. S. Shafir^ab

^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)

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DOI: https://doi.org/10.4213/tmf10520

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

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Linking options:

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:

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
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
M. V. Artemeva, M. O. Korpusov, “On the blow-up of the solution of a $(1+1)$ -dimensional thermal–electrical model”, Theoret. and Math. Phys., 219:2 (2024), 748–760
M. O. Korpusov, R. S. Shafir, A. K. Matveeva, “Numerical Diagnostics of Solution Blow-Up in a Thermoelectric Semiconductor Model”, Comput. Math. and Math. Phys., 64:7 (2024), 1595
M. V Artemeva, M. O Korpusov, “THE CAUCHY PROBLEM FOR AN NONLINEAR WAVE EQUATION”, Differencialʹnye uravneniâ, 60:10 (2024), 1299
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
M. O. Korpusov, R. S. Shafir, A. K. Matveeva, “Numerical diagnostics of solution blow-up in a thermoelectric semiconductor model”, Comput. Math. Math. Phys., 64:7 (2024), 1595–1602
M. V. Artemeva, M. O. Korpusov, “The Cauchy Problem for a Nonlinear Wave Equation”, Diff Equat, 60:10 (2024), 1369

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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Full-text PDF :	31
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References:	37
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