Weakly nonlinear asymptotics of the kappa-theta model of cellular flames: the Q-S equation
Claude-Michel Brauner
Université de Bordeaux I, Talence, FranceMichael L. Frankel
Indiana University Purdue University Indianapolis, USAJosephus Hulshof
Vrije Universiteit, Amsterdam, NetherlandsGregory I. Sivashinsky
Tel-Aviv University, Israel
![Weakly nonlinear asymptotics of the kappa-theta model of cellular flames: the Q-S equation cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-ifb-volume-7-issue-2.png&w=3840&q=90)
Abstract
We consider a quasi-steady version of the - model of flame front dynamics introduced in [FGS03] . In this case the mathematical model reduces to a single integro-differential equation. We show that a periodic problem for the latter equation is globally well-posed in Sobolev spaces of periodic functions. We prove that near the instability threshold the solutions of the equation are arbitrarily close to these of the Kuramoto–Sivashinsky equation on a fixed time interval if the evolution starts from close configurations. We present numerical simulations that illustrate the theoretical results, and also demonstrate the ability of the quasi-steady equation to generate chaotic cellular dynamics.
Cite this article
Claude-Michel Brauner, Michael L. Frankel, Josephus Hulshof, Gregory I. Sivashinsky, Weakly nonlinear asymptotics of the kappa-theta model of cellular flames: the Q-S equation. Interfaces Free Bound. 7 (2005), no. 2, pp. 131–146
DOI 10.4171/IFB/117