Rakib-Sivashinsky and Michelson-Sivashinsky Equations for Upward   Propagating Flames: A Comparison Analysis
  We establish a comparison between Rakib--Sivashinsky and Michelson-Sivashinsky quasilinear parabolic differential equations governing the weak thermal limit of upward flame front propagating in a channel. For the former equation, we give a complete description of all steady solutions and present their local and global stability analysis. For the latter, multi-coalescent unstable steady solutions are introduced and shown to be exponentially more numerous than the previous known coalescente solutions. This fact is argued to be responsible for the disagreement of the observed dynamics in numerical experiments with the exact (linear) stability analysis and also gives the ingredients to describe the quasi-stable behavior of parabolic steadily propagating flame with centered tip. 
Leonardo F. Guidi (1) and Domingos H. U. Marchetti (1) ((1) Instituto   de Fisica - Universidade de Sao Paulo - Sao Paulo - ...