On the existence of high Lewis number combustion fronts

We study a mathematical model for high Lewis number combustion processes with the reaction rate of the form of an Arrhenius law with or without an ignition cut-off. An efficient method for the proof of the existence and uniqueness of combustion fronts is provided by geometric singular perturbation theory. The fronts supported by the model with very large Lewis numbers are small perturbations of the front supported by the model with infinite Lewis number.