2002/03/08 by Leonardo F. Guidi, Guidi, Leonardo F., Domingos H. U. Marchetti +1
Engineering · Mathematics · Physics and Astronomy · #35B10 #35B32 #35B35 #35K55 #37N10 #Analysis of PDEs (math.AP) #Combustion and Detonation Processes #Combustion and flame dynamics #FOS: Mathematics #FOS: Physical sciences #Lightning and Electromagnetic Phenomena #Mathematical Physics (math-ph) #math-ph #math.AP #math.MP #msc:35B10 #msc:35B32 #msc:35B35 #msc:35K55 #msc:37N10
paper · pdf · doi:10.48550/arxiv.math/0203089
17 pages, 3 figures
arxiv created 2002/03/08 · openalex publication_date 2002/03/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.