Quenching and propagation in KPP reaction-diffusion equations with a heat loss

We consider a reaction-diffusion system of KPP type in a shear flow and with a non-zero heat-loss parameter. We establish criteria for the flame blow-off and propagation, and identify the propagation speed in terms of the exponential decay of the initial data. We prove the existence of travelling fronts for all speeds c > max(0, c*) in the case Le = 1, where c* is an element of R. This seems to be one of the first non-perturbative results on the existence of fronts for the thermo-diffusive system in higher dimensions.