The existence of a global attractor
for a Kuramoto-Sivashinsky type equation in 2D
Aslihan Demirkaya - Department of Mathematics, University of Kansas, 1460 Jayhawk Blvd, Lawrence, KS 66045-7523, United States (email)
Abstract: We consider a variation of the Kuramoto-Sivashinsky Equation in space dimension two. We show that under some assumptions the equation is globally well-posed and posseses a global attractor in the periodic case. The analysis is based on the Lyapunov function approach, point dissipativeness and asymptotic compactness.
Keywords: Kuramoto- Sivashinsky Equation, Attractors
Received: July 2008; Revised: April 2009; Published: September 2009.