Duan Jinqiao, Ervin Vincent, Gao Hongjun
Trajectory and Attractor Convergence for a Nonlocal Kuramoto-Sivashinsky Equation
(19K, LaTeX)
ABSTRACT. The nonlocal Kuramoto-Sivashinsky equation arises
in the modeling of the flow
of a thin film of viscous liquid falling down an inclined plane,
subject to an applied electric field.
In this paper, the authors show that, as
the coefficient of the nonlocal integral term goes to zero,
the solution trajectories and the maximal attractor
of the nonlocal Kuramoto-Sivashinsky equation converge to
those of the usual Kuramoto-Sivashinsky equation.