JournalsjemsVol. 13, No. 2pp. 345–390

Uniqueness and stability properties of monostable pulsating fronts

  • François Hamel

    Université d'Aix-Marseille, France
  • Lionel Roques

    INRA, Avignon, France
Uniqueness and stability properties of monostable pulsating fronts cover

Abstract

We prove the uniqueness, up to shifts, of pulsating traveling fronts for reaction-diffusion equations in periodic media with Kolmogorov–Petrovskiĭ–Piskunov type nonlinearities. These results provide in particular a complete classification of all KPP pulsating fronts. Furthermore, in the more general case of monostable nonlinearities, we also derive several global stability properties and convergence to pulsating fronts for solutions of the Cauchy problem with front-like initial data. In particular, we prove the stability of KPP pulsating fronts with minimal speed, which is a new result even in the case when the medium is invariant in the direction of propagation.

Cite this article

François Hamel, Lionel Roques, Uniqueness and stability properties of monostable pulsating fronts. J. Eur. Math. Soc. 13 (2010), no. 2, pp. 345–390

DOI 10.4171/JEMS/256