Global existence and blow-up of weak solutions for a fourth-order parabolic equation with gradient nonlinearity

This article deals with the behaviors of solutions to the initial-boundary value problem for a fourth-order parabolic equation with gradient nonlinearity. More precisely, we first get a threshold result for the solutions to exist globally or to blow up in finite time when the initial energy is subcritical and critical, and give an upper bound estimate of the lifespan. Furthermore, we derive the sufficient conditions for the existence of global and blow-up solutions for supercritical initial energy. Finally, we also give a lower bound estimate of the lifespan and obtain some estimates for blow-up rate. These results extend and improve some recent results.