Differential and Integral Equations

Exponential integrability of temperature in the thermistor problem

Xiangsheng Xu

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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.

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