Instabilities in a combustion model with two free interfaces

2018/07/06 by Davide Addona, Claude-Michel Brauner, Addona, Davide +5
Engineering · Mathematics · #35K50 #80A25 #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations #Primary: 35R35 #Secondary: 35B35 #Stability and Controllability of Differential Equations #math.AP #msc:35B35 #msc:35K50 #msc:35R35 #msc:80A25

paper · pdf · doi:10.48550/arxiv.1807.02462

arxiv created 2018/07/06 · openalex publication_date 2018/07/06 · arxiv updated 2018/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study in a strip of \mathbb R² a combustion model of flame propagation with stepwise temperature kinetics and zero-order reaction, characterized by two free interfaces, respectively the ignition and the trailing fronts. The latter interface presents an additional difficulty because the non-degeneracy condition is not met. We turn the system to a fully nonlinear problem which is thoroughly investigated. When the width ℓ of the strip is sufficiently large, we prove the existence of a critical value Le_c of the Lewis number Le, such that the one-dimensional, planar, solution is unstable for 0<Le<Le_c. Some numerical simulations confirm the analysis.

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