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arXiv · 1901.01123

Stability analysis and Hopf bifurcation at high Lewis number in a combustion model with free interface

Claude-Michel Brauner·Luca Lorenzi·Mingmin Zhang
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Abstract

In this paper we analyze the stability of the traveling wave solution for an ignition-temperature, first-order reaction model of thermo-diffusive combustion, in the case of high Lewis numbers (${\rm Le} >1$). The system of two parabolic PDEs is characterized by a free interface at which ignition temperature $\Theta_i$ is reached. We turn the model to a fully nonlinear problem in a fixed domain. When the Lewis number is large, we define a bifurcation parameter $m=\Theta_i/(1-\Theta_i)$ and a perturbation parameter $\varepsilon= 1/{\rm Le}$. The main result is the existence of a critical value $m^c(\varepsilon)$ close to $m^c=6$ at which Hopf bifurcation holds for $\varepsilon$ small enough. Proofs combine spectral analysis and non-standard application of Hurwitz Theorem with asymptotics as $\varepsilon\to 0$.

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Claude-Michel Brauner, Luca Lorenzi, Mingmin Zhang. 2019-01-04. Stability analysis and Hopf bifurcation at high Lewis number in a combustion model with free interface. https://arxiv.org/abs/1901.01123

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