Rakib-Sivashinsky and Michelson-Sivashinsky Equations for Upward Propagating Flames: A Comparison Analysis

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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.
17 pages, 3 figures

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Analysis of PDEs, Mathematical Physics, 35K55;35B10;35B35;35B32;37N10

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http://salesiana.dossiersoluciones.com/handle/123456789/63531

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0203089
 http://arxiv.org/abs/math/0203089

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arXiv