A fully nonlinear equation for the flame front in a quasi-steady combustion model

Claude Michel Brauner*, Josephus Hulshof, Luca Lorenzi, Gregory I. Sivashinsky

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We revisit the Near Equidiffusional Flames (NEF) model introduced by Matkowsky and Sivashinsky in 1979 and consider a simplified, quasisteady version of it. This simplification allows, near the planar front, an explicit derivation of the front equation. The latter is a pseudodifferential fully nonlinear parabolic equation of the fourth-order. First, we study the (orbital) stability of the null solution. Second, introducing a parameter ε, we rescale both the dependent and independent variables and prove rigourously the convergence to the solution of the Kuramoto-Sivashinsky equation as ε → 0.

Original languageEnglish
Pages (from-to)1415-1446
Number of pages32
JournalDiscrete and Continuous Dynamical Systems
Volume27
Issue number4
DOIs
StatePublished - Aug 2010

Keywords

  • Front dynamics
  • Fully nonlinear equations
  • Kuramoto-Sivashinsky equation
  • Pseudo-differential operators
  • Stability

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