Universal bounds for quasilinear parabolic equations with convection
Ryuichi Suzuki · Discrete and Continuous Dynamical Systems · 2006
We prove a universal bound, independent of the initial data, for all globalnonnegative solutions of the Dirichlet problem of thequasilinear parabolic equationwith convection$u_t = \Delta u^m +a\cdot abla u^q+ u^p$in $\Omega\times (0,\infty)$, where $\Omega$ is a smoothly bounded domain in $\mathbf{R^N}$, $a \in \mathbf {R^N}$, $ 1 \le m $ (N+1 )/[(m-1)(N+1)+2]$,which describes the initial blow-up rates of solutions.