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arXiv · 0910.5322

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

C. -M. Brauner·J. Hulshof·L. Lorenzi·G. I. Sivashinsky
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Abstract

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 $ε$, we rescale both the dependent and independent variables and prove rigourously the convergence to the solution of the Kuramoto-Sivashinsky equation as $ε\to 0$.

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C. -M. Brauner, J. Hulshof, L. Lorenzi, G. I. Sivashinsky. 2009-10-28. A fully nonlinear equation for the flame front in a quasi-steady combustion model. https://arxiv.org/abs/0910.5322

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