A class of fourth-order parabolic equation with arbitrary initial energy

摘要

In this paper we apply the modified potential well method to the study of the long time behaviors of solutions to a class of fourth-order parabolic equation in a bounded smooth domain of R-n for arbitrary n = 1. Global existence and blow up in finite time of solutions are obtained when the initial data satisfy different conditions. To be a little more precise, we give a threshold result for the solutions to exist globally or to blow up in finite time when the initial energy is subcritical and critical, respectively. Moreover, the decay rate of the L-2 norm is also obtained for global solutions. Sufficient conditions for the existence of global and blow-up solutions are also provided for supercritical initial energy. These improve and generalize some recent results. (C) 2018 Elsevier Ltd. All rights reserved.