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2004 Exponential integrability of temperature in the thermistor problem
Xiangsheng Xu
Differential Integral Equations 17(5-6): 571-582 (2004).

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.

Citation

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Xiangsheng Xu. "Exponential integrability of temperature in the thermistor problem." Differential Integral Equations 17 (5-6) 571 - 582, 2004.

Information

Published: 2004
First available in Project Euclid: 21 December 2012

zbMATH: 1174.35327
MathSciNet: MR2054935

Subjects:
Primary: 35K55
Secondary: 35B65 , 35K65

Rights: Copyright © 2004 Khayyam Publishing, Inc.

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Vol.17 • No. 5-6 • 2004
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