## Advances in Differential Equations

### The speed of propagation for KPP reaction-diffusion equations within large drift

#### Abstract

This paper is devoted to the study of the asymptotic behaviors of the minimal speed of propagation of pulsating travelling 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 [3] 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.

#### Article information

Source
Adv. Differential Equations, Volume 16, Number 3/4 (2011), 361-400.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355854312

Mathematical Reviews number (MathSciNet)
MR2767082

Zentralblatt MATH identifier
1219.35033

#### Citation

El Smaily, Mohammad; Kirsch, Stéphane. The speed of propagation for KPP reaction-diffusion equations within large drift. Adv. Differential Equations 16 (2011), no. 3/4, 361--400. https://projecteuclid.org/euclid.ade/1355854312