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 (Le>1). The system of
two parabolic PDEs is characterized by a free interface at which ignition
temperature Θi 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=Θi/(1−Θi) and a perturbation parameter
ε=1/Le. The main result is the existence of a critical value
mc(ε) close to mc=6 at which Hopf bifurcation holds for
ε small enough. Proofs combine spectral analysis and non-standard
application of Hurwitz Theorem with asymptotics as ε→0