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

被引：0

作者：

Brauner, C. -M. ^{[1
]}

Frankel, M.

Hulshof, J.

Roytburd, V.

机构：

[1] Univ Bordeaux 1, Math Appl Bordeaux, F-33405 Talence, France

[2] Indiana Univ Purdue Univ, Dept Math Sci, Indianapolis, IN 46202 USA

[3] Vrije Univ Amsterdam, Fac Sci, Div Math & Comp Sci, NL-1081 HV Amsterdam, Netherlands

[4] Rensselaer Polytech Inst, Dept Math Sci, Troy, NY 12180 USA

来源：

INTERFACES AND FREE BOUNDARIES | 2006年 / 8卷 / 03期

关键词：

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We continue the study of 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 relationships with the Kuramoto - Sivashinsky and Burgers - Sivashinsky equations.

引用

页码：301 / 316

页数：16

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