Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Global attractor and inertial sets for a nonlocal Kuramoto-Sivashinsky equation

Pages: 557 - 580, Volume 10, Issue 1/2, January/February 2004      doi:10.3934/dcds.2004.10.557

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D. Hilhorst - Analyse Numérique et EDP, CNRS, Université de Paris Sud, F-91405 Orsay, Cedex, France (email)
L. A. Peletier - Mathematical Institute, PB 9512, 2300 RA, Leiden, Netherlands (email)
A. I. Rotariu - Mathematical Institute, PB 9512, 2300 RA, Leiden, Netherlands (email)
G. Sivashinsky - School of Mathematical Sciences, Tel Aviv University, Israel (email)

Abstract: We consider a nonlinear fourth order parabolic equation with a nonlocal term which describes the time evolution of a flame front. After having established the existence of a global attractor for a corresponding boundary value problem, we prove the existence of inertial sets.

Keywords:  Kuramoto-Sivashinsky Equation, Dynamical Systems, Global Attractors, Inertial Sets.
Mathematics Subject Classification:  35K30, 35B40, 35B45.

Received: November 2001;      Revised: September 2003;      Available Online: October 2003.