Finite time blow-up for a thin-film equation with initial data at arbitrary energy level

In this paper, we consider the initial boundary value problem for a class of thin-film equations in Rn with a p-Laplace term and a nonlocal source term |u|q−2u−1|Ω|∫Ω|u|q−2udx. We prove that there exist weak solutions for the problem with arbitrarily initial energy that blow up in finite time. We also obtain the upper bounds for the blow-up time.