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.
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This work was supported by the Russian Science Foundation (grant No. 23-11-00056).
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Translated from Teoreticheskaya i Matematicheskaya Fizika, 2023, Vol. 217, pp. 378–390 https://doi.org/10.4213/tmf10520.
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Korpusov, M.O., Perlov, A.Y., Timoshenko, A.V. et al. Global-in-time solvability of a nonlinear system of equations of a thermal–electrical model with quadratic nonlinearity. Theor Math Phys 217, 1743–1754 (2023). https://doi.org/10.1134/S0040577923110090
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DOI: https://doi.org/10.1134/S0040577923110090