The existence of a global attractor for a Kuramoto-Sivashinsky type equation in 2D

Pages: 198 - 207, Issue Special, September 2009

 Abstract        Full Text (178.6K)              

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
Mathematics Subject Classification:  Primary: 35B41, 37L30; Secondary: 35B40

Received: July 2008;      Revised: April 2009;      Published: September 2009.