Lewis number

Bubble

Quantum mechanics

Hopf bifurcation

Pure mathematics

Bifurcation

Mathematical physics

Materials science

Stability (learning theory)

Perturbation (astronomy)

Computer science

Maximum bubble pressure method

Physical chemistry

Physics

Nonlinear system

Organic chemistry

Mathematics

Interface (matter)

Combustion

Domain (mathematical analysis)

Mathematical analysis

Chemistry

Mechanics

Machine learning

Annales de l Institut Henri Poincaré C Analyse Non Linéaire

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 $\varepsilon\to 0$.

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