- Turkish Journal of Mathematics
- Vol: 43 Issue: 3
- A blow-up result for nonlocal thin-film equation with positive initial energy
A blow-up result for nonlocal thin-film equation with positive initial energy
Authors : Mustafa Polat
Pages : 1797-1807
View : 10 | Download : 4
Publication Date : 9999-12-31
Article Type : Makaleler
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