中文摘要：

本文考虑了热电学模型中的热量散失现象，这一模型被称为欧姆热问题．在该模型中，两个导体被串联在一个两端具有恒定电势差的闭合电路中，当电流通过导体时，导体会产生热量．而这两个导体的电阻率均依赖于导体的温度．在该问题的数学描述中，两个导体温度的模型是一个齐次狄利克雷边界条件下的半线性的非局部抛物方程组．

英文摘要：

In this paper, we consider the phenomena of the thermal runaway in a thermal-electricity mod el, which is so-called an Ohmic heating model. The model prescribes the dimensionless temperature when the electric current flows through two conductors A and B, subject to a fixed potential difference. The electrical resistivities to the two conductors both depend on their temperature. The problem will be formulated into a semilinear nonlocal parabolic equations with Dirichlet boundary conditions mathematically.