Blowup time estimates for a parabolic p-Laplacian equation with nonlinear gradient terms

Abstract

This article studies the blowup time of weak solutions to the degenerate parabolic equation $$u_{t}-\Delta _{p}u=\lambda u^{m}+\mu |\nabla u|^{q}$$ with homogeneous Dirichlet boundary condition in a bounded smooth domain. We first obtain an upper bound and a lower one for the blowup time of $$L^{\infty }$$ blowup solutions and then get the upper bound for the blowup time of gradient blowup solutions.