Global existence and finite time blow-up of the solution for a thin-film equation with high initial energy.

This paper is devoted to the study of a thin-film equation, which was considered extensively in recent years. We obtain the conditions for global existence and finite time blow-up of solution for the high initial energy case, i.e., J ( u 0 ) > d , while the previous works only considered the case J ( u 0 ) ≤ d , here d is the mountain pass level. Moreover, for the blow-up solution with J ( u 0 ) < d , we obtain the lower bound estimate of the blow-up time and blow-up rate. [ABSTRACT FROM AUTHOR]