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

International audienceWe consider a reaction-diffusion system of the 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 existence of traveling fronts for all speeds $c>\hbox{max}(0,c^*)$ in the case $Le=1$, where $c^*\in\mathbb{R}$. That seems to be one of the first non-perturbative results on the existence of fronts for the thermo-diffusive system in higher dimensions