Propagation speed for reaction–diffusion equations in general domains

Henri Berestycki; François Hamel; Nikolai Nadirashvili

doi:10.1016/j.crma.2004.05.020

Partial Differential Equations

Propagation speed for reaction–diffusion equations in general domains

Presented by: Haïm Brezis

Henri Berestycki ¹; François Hamel ²; Nikolai Nadirashvili ³

¹ EHESS, CAMS, 54, boulevard Raspail, 75006 Paris, France
² Université Aix-Marseille III, LATP, avenue Esc. Normandie-Niemen, 13397 Marseille cedex 20, France
³ University of Chicago, Department of Mathematics, 5734, S. University Avenue, Chicago, IL 60637-1546, USA

Comptes Rendus. Mathématique, Volume 339 (2004) no. 3, pp. 163-168.

Abstract
Résumé

This Note is devoted to the analysis of some propagation phenomena for reaction–diffusion–advection equations with Fisher or Kolmogorov–Petrovsky–Piskunov (KPP) type nonlinearities. Some formulæ for the speed of propagation of pulsating fronts in periodic domains are given. These allow us to describe the influence of the various terms in the equation or of geometry on propagation. We also derive results for propagation speed in more general domains without periodicity.

Cette Note est consacrée à l'analyse de phénomènes de propagation pour des équations de réaction–diffusion–advection du type Fisher ou Kolmogorov–Petrovsky–Piskunov (KPP). On donne des formules pour les vitesses de propagation de fronts pulsatoires dans des domaines périodiques. Celles-ci permettent de mettre en lumière l'influence des différents termes de l'équation ou de la géométrie sur la propagation. On considère également le cas de domaines généraux.

Received: 2004-05-25
Published online: 2004-07-23

DOI: 10.1016/j.crma.2004.05.020

Author's affiliations:

Henri Berestycki ¹; François Hamel ²; Nikolai Nadirashvili ³

¹ EHESS, CAMS, 54, boulevard Raspail, 75006 Paris, France
² Université Aix-Marseille III, LATP, avenue Esc. Normandie-Niemen, 13397 Marseille cedex 20, France
³ University of Chicago, Department of Mathematics, 5734, S. University Avenue, Chicago, IL 60637-1546, USA

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     author = {Henri Berestycki and Fran\c{c}ois Hamel and Nikolai Nadirashvili},
     title = {Propagation speed for reaction{\textendash}diffusion equations in general domains},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {163--168},
     publisher = {Elsevier},
     volume = {339},
     number = {3},
     year = {2004},
     doi = {10.1016/j.crma.2004.05.020},
     language = {en},
}

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Henri Berestycki; François Hamel; Nikolai Nadirashvili. Propagation speed for reaction–diffusion equations in general domains. Comptes Rendus. Mathématique, Volume 339 (2004) no. 3, pp. 163-168. doi : 10.1016/j.crma.2004.05.020. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.05.020/

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