准稳态燃烧模型中火焰阵面的完全非线性方程
A fully nonlinear equation for the flame front in a quasi-steady combustion model
摘要：
我们重新审视了Matkowsky和Sivashinsky在1979年提出的近等扩散火焰（NEF）模型，并考虑了它的简化、准稳态版本。这种简化允许在平面锋面附近显式推导锋面方程。后者是一个四阶拟微分完全非线性抛物型方程。首先，我们研究零解的（轨道）稳定性。其次，引入参数$ε$，对自变量和因变量进行重新标度，严格证明了Kuramoto-Sivashinsky方程解的收敛性为$ε\to 0$ .
英文摘要：
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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