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

Claude-Michel Brauner | Zendy; Josephus Hulshof | Zendy; Luca Lorenzi | Zendy; Gregory Sivashinsky | Zendy

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

Author(s) -

Claude-Michel Brauner,

Josephus Hulshof,

Luca Lorenzi,

Gregory Sivashinsky

Publication year - 2010

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2010.27.1415

Subject(s) - flame front , nonlinear system , convergence (economics) , front (military) , combustion , planar , mathematical analysis , mathematics , stability (learning theory) , physics , mechanics , computer science , meteorology , chemistry , quantum mechanics , computer graphics (images) , organic chemistry , machine learning , turbulence , economics , economic growth

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

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