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Comptes Rendus Mathématique
Volume 348, n° 15-16
pages 857-861 (août 2010)
Doi : 10.1016/j.crma.2010.07.007
Received : 20 April 2010 ;  accepted : 8 July 2010
Asymptotics of the KPP minimal speed within large drift
Asymptotiques de la vitesse minimale KPP dans le cas d'une grande advection
 

Mohammad El Smaily , Stéphane Kirsch
Department of Mathematics, University of British Columbia & Pacific Institute for the Mathematical Sciences, 1984 Mathematics Road, V6T 1Z2, Vancouver, BC, Canada 

Abstract

This Note is concerned with the asymptotic behavior of the minimal KPP speed of propagation for reaction–advection–diffusion equations with a large drift Mq (where q is the advection). We first give the limit of the speed as   in any space dimension N . Then, we give the necessary and sufficient condition that the advection field should satisfy so that the speed acts as   as  .

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Résumé

Dans cette Note on étudie le comportement asymptotique de la vitesse minimale de propagation des fronts progressifs pulsatoires satisfaisant une équation de réaction–advection–diffusion dans le cas d'une grande advection Mq (où q est l'advection). On donne la valeur limite de la vitesse lorsque   dans un espace de dimension N quelconque. Pour le cas   on donne une condition nécessaire et suffisante pour que la vitesse se comporte comme   pour  .

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