On the κ-θ model of cellular flames: Existence in the large and asymptotics

Claude Michel Brauner*, Michael L. Frankel, Josephus Hulshof, Alessandra Lunardi, Gregory I. Sivashinsky

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the κ-θ model of flame front dynamics introduced in [6]. We show that a space-periodic problem for the latter system of two equations is globally well-posed. We prove that near the instability threshold the front is arbitrarily close to the solution of the Kuramoto-Sivashinsky equation on a fixed time interval if the evolution starts from close configurations. The dynamics generated by the model is illustrated by direct numerical simulation.

Original languageEnglish
Pages (from-to)29-39
Number of pages11
JournalDiscrete and Continuous Dynamical Systems - Series S
Volume1
Issue number1
DOIs
StatePublished - Mar 2008

Keywords

  • Combustion
  • Front dynamics
  • Kuramoto - Sivashinsky equation
  • Premixed flames

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