Global existence and blow-up phenomena for nonlinear divergence form parabolic equations with inhomogeneous Neumann boundary conditions

Abstract

In this paper, we consider nonlinear divergence form parabolic equations with inhomogeneous Neumann boundary conditions. We establish respectively the conditions on nonlinearities to guarantee that u ( x , t ) exists globally or blows up at some finite time. If blow-up occurs, we obtain upper and lower bounds of the blow-up time.