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

Aslihan Demirkaya

doi:10.3934/proc.2009.2009.198

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2009, Volume 2009: 198-207. Doi: 10.3934/proc.2009.2009.198 open access

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

Aslihan Demirkaya^1,

1.
Department of Mathematics, University of Kansas, 1460 Jayhawk Blvd, Lawrence, KS 66045-7523

Received: June 30, 2008

Revised: March 31, 2009

Published: August 2009

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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.

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

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