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

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January & February 2004, 10(1&2): 557-580. doi: 10.3934/dcds.2004.10.557

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

D. Hilhorst ^1, , L. A. Peletier ^2, , A. I. Rotariu ^2, and G. Sivashinsky ^3,

1.	Analyse Numérique et EDP, CNRS, Université de Paris Sud, F-91405 Orsay, Cedex, France
2.	Mathematical Institute, PB 9512, 2300 RA, Leiden, Netherlands, Netherlands
3.	School of Mathematical Sciences, Tel Aviv University, Israel

Received November 2001 Revised September 2003 Published October 2003

Abstract
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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: Global Attractors, Inertial Sets., Kuramoto-Sivashinsky Equation, Dynamical Systems.

Mathematics Subject Classification: 35K30, 35B40, 35B4.

Citation: D. Hilhorst, L. A. Peletier, A. I. Rotariu, G. Sivashinsky. Global attractor and inertial sets for a nonlocal Kuramoto-Sivashinsky equation. Discrete & Continuous Dynamical Systems - A, 2004, 10 (1&2) : 557-580. doi: 10.3934/dcds.2004.10.557

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