Global existence and blow-up phenomena for p-Laplacian heat equation with inhomogeneous Neumann boundary conditions

In this paper, we consider a p-Laplacian heat equation with inhomogeneous Neumann boundary condition. We establish respectively the conditions on the nonlinearities to guarantee that the solution 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 by differential inequalities.