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

Authors: MUSTAFA POLAT

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.

Keywords: Nonlinear thin film equation, positive initial energy, blow up, periodic boundary condition, Non-local source term

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