Mathematics – Analysis of PDEs
Scientific paper
2009-09-05
Advances in Differential Equations, Volume 16, Numbers 3-4, (2011), pp. 361-400
Mathematics
Analysis of PDEs
Scientific paper
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.
Kirsch Stephane
Smaily Mohammad El
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