# Instabilities in a combustion model with two free interfaces

Source: [Instabilities in a combustion model with two free interfaces](<https://www.sota2.com/research/paper/68fa54fb1e209131ce990067>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T13:18:36.524Z

Authors: Davide Addona, Claude-Michel Brauner, Luca Lorenzi, Wen Zhang

Published: 2018-07-06T15:48:32.000Z

## Abstract

We study in a strip of $\\mathbb R^2$ 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 $\\ell$ 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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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1807.02462>)

[PDF](<https://arxiv.org/pdf/1807.02462.pdf>)