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Exponential integrability of temperature in the thermistor problem. (English) Zbl 1174.35327

Summary: We consider weak solutions to the initial-boundary-value problem for the system \(\frac {\partial u}{\partial t}-\operatorname {div}(K(u)\nabla u)=\sigma (u)| \nabla \varphi | ^2\), \(\operatorname {div}(\sigma (u)\nabla \varphi )=0\) in the case where \(K(u)\) and \(\sigma (u)\) may both tend to 0 as \(u\to \infty \). 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.

MSC:

35B65 Smoothness and regularity of solutions to PDEs
35K65 Degenerate parabolic equations
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