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.
Citation
Mohammad El Smaily. Stéphane Kirsch. "The speed of propagation for KPP reaction-diffusion equations within large drift." Adv. Differential Equations 16 (3/4) 361 - 400, March/April 2011. https://doi.org/10.57262/ade/1355854312
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