Pré-Publication, Document De Travail Année : 2009

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

Résumé

We revisit the Near Equidiffusional Flames (NEF) model introduced by Matkowsky and Sivashinsky in 1979 and consider a simplified, quasi-steady 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 $\varepsilon$, we rescale both the dependent and independent variables and prove rigourously the convergence to the solution of the Kuramoto-Sivashinsky equation as $\varepsilon \to 0$.

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hal-00426859 , version 1 (28-10-2009)

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  • HAL Id : hal-00426859 , version 1

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Claude-Michel Brauner, Josephus Hulshof, Luca Lorenzi, G.I. Sivashinsky. A fully nonlinear equation for the flame front in a quasi-steady combustion model. 2009. ⟨hal-00426859⟩
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