A Comparison Analysis of Sivashinsky's Type Evolution Equations Describing Flame Propagation in Channels (in collaboration with Leonardo Guidi) Resumo: We establish a comparison between Rakib--Sivashinsky and Michelson--Sivashinsky quasilinear parabolic differential equations governing the weak thermal limit of flame front propagating in channels [GM]. For the former equation, based in [GM1], a complete description of all steady solutions is given and local and global stability are presented. These analysis complement the work of Berestycki et al [BKS]. For the latter, bi--coalescent and interpolating unstable steady solutions are introduced and shown to be more numerous than the previous known coalescent solutions. These facts are argued to be responsible for the disagreement between the observed dynamics in numerical experiments and the exact (linear) stability analysis by Vaynblat and Matalon [VM] and give ingredients to construct metastable solutions describing parabolic steadily propagating flame with centered tip. [BKS] H. Berestycki, S. Kamin and G. Sivashinsky} (2001) Metastability in a flame front evolution equation, Interfaces and Free Boundaries 3, 361-392. [GM] L. F. Guidi and D. H. U. Marchetti} (2003) A Comparison Analysis of Sivashinsky's Type Evolution Equations Describing Flame Propagation in Channels, Phys. Lett. A 308, 162-172. [GM1] L. F. Guidi and D. H. U. Marchetti} (2001) Renormalization Group Flow of the Two-Dimensional Hierarchical Coulomb Gas, Commun. Math. Phys. 219, 671-702. [VM] D. Vaynblat and M. Matalon} (2000) Stability of POle Solutions for Planar Propagating Flames: I. Exact Eigenvalues and Eigenfunctions, SIAM J. Appl. Math. 60, 679.