Differential and Integral Equations

Exponential integrability of temperature in the thermistor problem

Xiangsheng Xu

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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

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

First available in Project Euclid: 21 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K55: Nonlinear parabolic equations
Secondary: 35B65: Smoothness and regularity of solutions 35K65: Degenerate parabolic equations


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

Export citation