%0 Journal Article
%T The speed of propagation for KPP reaction-diffusion equations within large drift
%A Mohammad El Smaily
%A Stephane Kirsch
%J Mathematics
%D 2009
%I arXiv
%X This paper is devoted to the study of the asymptotic behaviors of the minimal speed of propagation of pulsating traveling fronts solving the Fisher-KPP reaction-advection-diffusion equation within either a large drift, a mixture of large drift and small reaction, or a mixture of large drift and large diffusion. We consider a periodic heterogenous framework and we use the formula of Berestycki, Hamel and Nadirashvili \cite{bhn2} for the minimal speed of propagation to prove the asymptotics in any space dimension $N.$ We express the limits as the maxima of certain variational quantities over the family of "first integrals" of the advection field. Then, we perform a detailed study in the case N=2 which leads to a necessary and sufficient condition for the positivity of the asymptotic limit of the minimal speed within a large drift.
%U http://arxiv.org/abs/0909.0985v3