Duan, Jinqiao, and Ervin, Vincent
On the Stochastic Kuramoto-Sivashinsky Equation
(839K, Postscript)

ABSTRACT.  In this article we study the solution of the Kuramoto--Sivashinsky 
equation (for surface erosion or growth) 
on a bounded interval subject to a random forcing term. We 
show that a unique solution to the equation exists for all time and 
depends continuously on the initial data.