## Differential and Integral Equations

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

### Exponential integrability of temperature in the thermistor problem

#### 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

**Permanent link to this document**

https://projecteuclid.org/euclid.die/1356060348

**Mathematical Reviews number (MathSciNet)**

MR2054935

**Zentralblatt MATH identifier**

1174.35327

**Subjects**

Primary: 35K55: Nonlinear parabolic equations

Secondary: 35B65: Smoothness and regularity of solutions 35K65: Degenerate parabolic equations

#### Citation

Xu, Xiangsheng. Exponential integrability of temperature in the thermistor problem. Differential Integral Equations 17 (2004), no. 5-6, 571--582. https://projecteuclid.org/euclid.die/1356060348.