JournalsjemsVol. 7, No. 2pp. 173–213

The speed of propagation for KPP type problems. I: Periodic framework

  • Henry Berestycki

    Ecole des hautes études en sciences sociales, Paris, France
  • François Hamel

    Université d'Aix-Marseille, France
  • Nikolai Nadirashvili

    University of Chicago, USA
The speed of propagation for KPP type problems. I: Periodic framework cover
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Abstract

This paper is devoted to some nonlinear propagation phenomena in periodic and more general domains, for reaction-diffusion equations with Kolmogorov-Petrovsky-Piskunov (KPP) type nonlinearities. The case of periodic domains with periodic underlying excitable media is a follow-up of the article \cite{bh}. It is proved that the minimal speed of pulsating fronts is given by a variational formula involving linear eigenvalue problems. Some consequences concerning the influence of the geometry of the domain, of the reaction, advection and diffusion coefficients are given. The last section deals with the notion of asymptotic spreading speed. The main properties of the spreading speed are given. Some of them are based on some new Liouville type results for nonlinear elliptic equations in unbounded domains.

Cite this article

Henry Berestycki, François Hamel, Nikolai Nadirashvili, The speed of propagation for KPP type problems. I: Periodic framework. J. Eur. Math. Soc. 7 (2005), no. 2, pp. 173–213

DOI 10.4171/JEMS/26