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.

中文翻译：

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二次非线性热电模型非线性方程组的全局时间可解性

摘要

提出了电场电势和温度具有二次非线性的方程组来描述电路板的半导体元件的加热过程，随着时间的推移可能出现热和电“击穿”。对于该方程组，证明了时间不可延经典解的存在性，并且还获得了唯一的全局时间可解性的充分条件。