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
Xiangsheng Xu. "Exponential integrability of temperature in the thermistor problem." Differential Integral Equations 17 (5-6) 571 - 582, 2004. https://doi.org/10.57262/die/1356060348
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