5 papers
Escape Probability and Mean Residence Time in Random Flows with Unsteady Drift
Jinqiao Duan, James Brannan, Vincent Ervin
We investigate fluid transport in random velocity fields with unsteady drift. First, we propose to quantify fluid transport between flow regimes of different characteristic motion,…
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…