## 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