A FULLY NONLINEAR EQUATION FOR THE FLAME FRONT IN A QUASI-STEADY COMBUSTION MODEL

作者：Brauner Claude Michel^*; Hulshof Josephus; Lorenzi Luca; Sivashinsky Gregory I

来源：Discrete and Continuous Dynamical Systems, 2010, 27(4): 1415-1446.

DOI：10.3934/dcds.2010.27.1415

• Front dynamics
• stability
• Kuramoto-Sivashinsky equation
• fully nonlinear equations
• pseudo-differential operators

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

• 出版日期2010-8
• 单位厦门大学