Turkish Journal of Mathematics
DOI
10.3906/mat-1806-35
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
First Page
1797
Last Page
1807
Recommended Citation
POLAT, MUSTAFA
(2019)
"A blow-up result for nonlocal thin-film equation with positive initial energy,"
Turkish Journal of Mathematics: Vol. 43:
No.
3, Article 52.
https://doi.org/10.3906/mat-1806-35
Available at:
https://journals.tubitak.gov.tr/math/vol43/iss3/52
