  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
$\epsilon\to 0$.
