The evolution thermistor problem with degenerate thermal conductivity. (English) Zbl 1012.35047
The paper deals with weak solvability of the following time dependent thermistor problem with degenerate thermal conductivity
\[
\begin{cases} u_t -\nabla\cdot (a(u)\nabla u)=\sigma(u)|\nabla\varphi|^2 &\text{ in }Q=\Omega\times (0,T),\\ \nabla\cdot (\sigma(u)\nabla \varphi)=0 &\text{ in }Q,\\ u=0 &\text{ on }\partial\Omega\times(0,T),\\ \varphi=\varphi_0 &\text{ on }\partial\Omega\times(0,T),\\ u(\cdot,0)=u_0 &\text{ in }\Omega. \end{cases}
\]
{}.
Reviewer: Dian K.Palagachev (Bari)
MSC:
35K65 | Degenerate parabolic equations |
35J60 | Nonlinear elliptic equations |
78A35 | Motion of charged particles |