Stability and attractors for the quasi-steady equation of cellular flames
Victor Roytburd
Rensselaer Polytechnic Institute, Troy, USAMichael L. Frankel
Indiana University Purdue University Indianapolis, USAJosephus Hulshof
Vrije Universiteit, Amsterdam, NetherlandsClaude-Michel Brauner
Université de Bordeaux I, Talence, France

Abstract
We continue the study a simple integro-differential equation: the Quasi-Steady equation (QS) of flame front dynamics. This equation is dynamically similar to the Kuramoto-Sivashinsky (KS) equation. In \cite{FGS03}, where it was introduced, its well-posedness and proximity for finite time intervals to the KS equation in Sobolev spaces of periodic functions were established. Here we demonstrate that QS possesses a universal absorbing set, and a compact attractor. Furthermore we show that the attractor is of a finite Hausdorff dimension, and give an estimate on it. We discuss relationship with the Kuramoto-Sivashinsky and Burgers-Sivashinsky equations.
Cite this article
Victor Roytburd, Michael L. Frankel, Josephus Hulshof, Claude-Michel Brauner, Stability and attractors for the quasi-steady equation of cellular flames. Interfaces Free Bound. 8 (2006), no. 3, pp. 301–316
DOI 10.4171/IFB/145