# American Institute of Mathematical Sciences

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

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

 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

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.
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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