Pulsating traveling fronts in space-time periodic media

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 c >= c** 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. To cite this article: G. Nadin, C R. Acad. Sci. Paris, Ser. I 346 (2008). (C) 2008 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.