Global Existence and Finite Time Blow-up for the m-Laplacian Parabolic Problem

In this paper, we consider an initial boundary value problem of m-Laplacian parabolic equation arising in various physical models. We tackle this problem at three different initial energy levels. For the sub-critical initial energy, we obtain the blow-up result and estimate the lower and upper bounds of the blow-up time. For the critical initial energy, we show the global existence, asymptotic behavior, finite time blow-up and the lower bound of the blow-up time. For the sup-critical initial energy, we prove the finite time blow-up and estimate the lower and upper bounds of the blow-up time.