Instabilities in a combustion model with two free interfaces

We study in a strip of R2 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 ℓ of the strip is sufficiently large, we prove the existence of a critical value Lec of the Lewis number Le, such that the one-dimensional, planar, solution is unstable for 0