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 R-n with a p-Laplace term and a nonlocal source term vertical bar u vertical bar(q-2)u - 1/vertical bar Omega vertical bar integral(Omega) vertical bar u vertical bar(q-2)udx. 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. Crown Copyright (C) 2017 Published by Elsevier Inc. All rights reserved.