JournalsifbVol. 8 , No. 3DOI 10.4171/ifb/145

Stability and attractors for the quasi-steady equation of cellular flames

  • Victor Roytburd

    Rensselaer Polytechnic Institute, Troy, USA
  • Michael L. Frankel

    Indiana University Purdue University Indianapolis, USA
  • Josephus Hulshof

    Vrije Universiteit, Amsterdam, Netherlands
  • Claude-Michel Brauner

    Université de Bordeaux I, Talence, France
Stability and attractors for the quasi-steady equation of cellular flames cover

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.