## Differential and Integral Equations

### Exponential integrability of temperature in the thermistor problem

Xiangsheng Xu

#### Abstract

We consider weak solutions to the initial- boundary-value problem for the system $\frac{\partial u}{\partial t}- \mbox{div}(K(u)\nabla u) = \sigma(u)|\nabla \varphi|^2$, $\mbox{div}\left(\sigma(u)\nabla\varphi\right) =0$ in the case where $K(u)$ and $\sigma(u)$ may both tend to $0$ as $u\rightarrow \infty$. It is established that $u$ in the solution belongs to some Orlicz space under certain conditions. This implies that $u$ is exponentially integrable in some cases.

#### Article information

Source
Differential Integral Equations, Volume 17, Number 5-6 (2004), 571-582.

Dates
First available in Project Euclid: 21 December 2012