Advances in Differential Equations
- Adv. Differential Equations
- Volume 16, Number 3/4 (2011), 361-400.
The speed of propagation for KPP reaction-diffusion equations within large drift
Mohammad El Smaily and Stéphane Kirsch
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
Subjects
Primary: 35K55: Nonlinear parabolic equations 35K57: Reaction-diffusion equations 35B30: Dependence of solutions on initial and boundary data, parameters [See also 37Cxx] 35Q80: PDEs in connection with classical thermodynamics and heat transfer 35Q92: PDEs in connection with biology and other natural sciences 37C10: Vector fields, flows, ordinary differential equations 80A32: Chemically reacting flows [See also 92C45, 92E20]
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