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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
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.
Received: 16.04.2023 Revised: 25.05.2023
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
Linking options:
https://www.mathnet.ru/eng/tmf10520https://doi.org/10.4213/tmf10520 https://www.mathnet.ru/eng/tmf/v217/i2/p378
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