Geodesic
Stability and attractors for the quasi-steady equation of cellular flames
Claude-Michel Brauner1 ; Michael L. Frankel2 ; Josephus Hulshof3 ; Victor Roytburd4
1Université de Bordeaux I, Talence, France
2Indiana University Purdue University Indianapolis, USA
3Vrije Universiteit, Amsterdam, Netherlands
4Rensselaer Polytechnic Institute, Troy, USA
Interfaces and free boundaries, Tome 8 (2006) no. 3, pp. 301-316

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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 [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.
DOI : 10.4171/ifb/145
Classification : 35-XX, 65-XX, 76-XX, 92-XX

Claude-Michel Brauner  1   ; Michael L. Frankel  2   ; Josephus Hulshof  3   ; Victor Roytburd  4

1 Université de Bordeaux I, Talence, France
2 Indiana University Purdue University Indianapolis, USA
3 Vrije Universiteit, Amsterdam, Netherlands
4 Rensselaer Polytechnic Institute, Troy, USA 
Claude-Michel Brauner; Michael L. Frankel; Josephus Hulshof; Victor Roytburd. Stability and attractors for the quasi-steady equation of cellular flames. Interfaces and free boundaries, Tome 8 (2006) no. 3, pp. 301-316. doi: 10.4171/ifb/145
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     title = {Stability and attractors for the quasi-steady equation of cellular flames},
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     pages = {301--316},
     year = {2006},
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     doi = {10.4171/ifb/145},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/145/}
}
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