4 papers · 1 filter
On the Stochastic Kuramoto-Sivashinsky Equation
Jinqiao Duan, Vincent Ervin
In this article we study the solution of the Kuramoto-Sivashinsky equation (for surface erosion or surface growth) on a bounded interval subject to a random forcing term. We show t…
Asymptotic Dynamical Difference between the Nonlocal and Local Swift-Hohenberg Models
Guoguang Lin, Hongjun Gao, Jinqiao Duan +1
In this paper the difference in the asymptotic dynamics between the nonlocal and local two-dimensional Swift-Hohenberg models is investigated. It is shown that the bounds for the d…
Trajectory and Attractor Convergence for a Nonlocal Kuramoto-Sivashinsky Equation
Jinqiao Duan, Vincent Ervin, Hongjun Gao
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.…
Dynamics of a Nonlocal Kuramoto-Sivashinsky Equation
Jinqiao Duan, Vincent Ervin
In this paper we study the effects of a ``nonlocal'' term on the global dynamics of the Kuramoto-Sivashinsky equation. We show that the equation possesses a ``family of maximal att…