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 nonlocalsource term under the periodic boundary conditions. In particular, a finite time blow-up result is established for thecase of positive initial energy provided that $frac{pi^2}{a^2}leqfrac2{p-1}$, where a is the length of the interval and p > 1 is the power of nonlinear force term. Also upper and lower blow-uptimes are estimated.