Asymptotic behaviour of solutions of quasilinear parabolic equation with Robin boundary condition
Résumé
In this paper we study solutions of the quasi-linear parabolic equations ${{\partial u} \over {\partial t}} -\d _p u = a(x) |u|^{q-1}u$ in $(0,T) \times \O $ with Robin boundary condition ${{\p u } \over {\p \nu}}|\nabla u|^{p-2} = b(x) |u|^{r-1}u$ in $(0,T) \times \p \O$ where $\Omega$ is a regular bounded domain in $\R^N$, $N \geq 3$, $q>1$, $r>1$ and $p \geq 2$. Some sufficient conditions on $a$ and $b$ are obtained for those solutions to be bounded or blowing up at a finite time. Next we give the asymptotic behavior of the solution in special cases.
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