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

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_iis reached. We turn the model to a fully nonlinear problem in a fixed domain. When the Lewis number is large, we define a...