Archive for Rational Mechanics and Analysis

, Volume 157, Issue 2, pp 91–163

Travelling Fronts and Entire Solutions¶of the Fisher-KPP Equation in ℝN

  • François Hamel
  • Nikolaï Nadirashvili

DOI: 10.1007/PL00004238

Cite this article as:
Hamel, F. & Nadirashvili, N. Arch. Rational Mech. Anal. (2001) 157: 91. doi:10.1007/PL00004238

Abstract:

This paper is devoted to time-global solutions of the Fisher-KPP equation in ℝN:
$$$$
where f is a C2 concave function on [0,1] such that f(0)=f(1)=0 and f>0 on (0,1). It is well known that this equation admits a finite-dimensional manifold of planar travelling-fronts solutions. By considering the mixing of any density of travelling fronts, we prove the existence of an infinite-dimensional manifold of solutions. In particular, there are infinite-dimensional manifolds of (nonplanar) travelling fronts and radial solutions. Furthermore, up to an additional assumption, a given solution u can be represented in terms of such a mixing of travelling fronts.

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • François Hamel
    • 1
  • Nikolaï Nadirashvili
    • 2
  1. 1.CNRS, Université Pierre et Marie Curie¶Laboratoire d'Analyse Numérique, B.C. 187¶4 place Jussieu, 75252 Paris Cedex 05, FranceFR
  2. 2.University of Chicago, Department of Mathematics¶5734 University Avenue, Chicago, IL 60637-1546, USAUS

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