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

Henri Berestycki (1) , Francois Hamel (2) , Alexander Kiselev (3) , Leonid Ryzhik (4)

1 CAMS - Centre d'Analyse et de Mathématique sociales
2 LATP - Laboratoire d'Analyse, Topologie, Probabilités
3 University of Wisconsin-Madison
4 Department of Mathematics [Chicago]

We 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.

Mots clés: propagation; quenching; travelling fronts; boundary heat loss; thermodiffusive system

Domaines: Equations aux dérivées partielles [math.AP]

Henri Berestycki, Francois Hamel, Alexander Kiselev, Leonid Ryzhik. Quenching and propagation in KPP reaction-diffusion equations with a heat loss. Archive for Rational Mechanics and Analysis, 2005, pp.57. ⟨hal-00003739⟩