A blow-up result for nonlocal thin-film equation with positive initial energy

Abstract

In this note, we consider a thin-film equation including a diffusion term, a fourth order term and a nonlocal source term under the periodic boundary conditions. In particular, a finite time blow-up result is established for the case of positive initial energy provided that \[ \frac{\pi^2}{a^2}\leq \frac{2}{p-1},\] where $a$ is the length of the interval and $p>1$ is the power of nonlinear force term. Also upper and lower blow-up times are estimated.