Asymptotic Analysis in a Gas-Solid Combustion Model with Pattern   Formation
  We consider a free interface problem which stems from a solid-gas model in combustion with pattern formation. We derive a third-order, fully nonlinear, self-consistent equation for the flame front. Asymptotic methods reveal that the interface approaches a solution of the Kuramoto-Sivashinsky equation. Numerical results are presented which illustrate the dynamics. 
Claude-Michel Brauner, Lina Hu, Luca Lorenzi
math.AP