A class of fourth-order parabolic equation with arbitrary initial energy. (October 2018) - Han, Yuzhu
Abstract: 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.