Partial Differential Equations
Pulsating traveling fronts in space–time periodic media
Comptes Rendus. Mathématique, Volume 346 (2008) no. 17-18, pp. 951-956.

This Note deals with the existence of pulsating traveling fronts for some reaction–diffusion equation in space–time periodic media. Under some hypotheses, there exist two speeds c and c such that there exist some pulsating traveling fronts of speed c for all cc and that there exists no such front of speed c<c. In the case of a KPP-type reaction term, we characterize this speed with the help of a family of eigenvalues associated with the equation. Lastly, we study the dependence between this minimal speed and the coefficients of the equation.

Cette Note traite de l'existence de fronts pulsatoires pour une équation de réaction–diffusion en milieu périodique en temps et en espace. Sous certaines hypothèses, il existe deux vitesses c et c telles qu'il existe des fronts pulsatoires de vitesse c pour tout cc et qu'il n'existe pas de tel front de vitesse c<c. Dans le cas d'un terme de réaction de type KPP, nous caractérisons cette vitesse à l'aide d'une famille de valeurs propres associée à l'équation. Enfin, nous étudions la dépendance entre cette vitesse minimale et les coefficients de l'équation.

Accepted:
Published online:
DOI: 10.1016/j.crma.2008.07.030
Nadin, Grégoire 1, 2

1 Département de mathématiques et applications, École normale supérieure, 45, rue d'Ulm, 75230 Paris cedex 05, France
2 UPMC université Paris 6, Laboratoire Jacques-Louis Lions, 75252 Paris cedex 05, France
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Nadin, Grégoire. Pulsating traveling fronts in space–time periodic media. Comptes Rendus. Mathématique, Volume 346 (2008) no. 17-18, pp. 951-956. doi : 10.1016/j.crma.2008.07.030. http://www.numdam.org/articles/10.1016/j.crma.2008.07.030/

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