Communications in Mathematical Physics

, Volume 343, Issue 1, pp 207–232 | Cite as

The Shape of Expansion Induced by a Line with Fast Diffusion in Fisher-KPP Equations

  • Henri Berestycki
  • Jean-Michel Roquejoffre
  • Luca Rossi
Article

Abstract

We establish a new property of Fisher-KPP type propagation in a plane, in the presence of a line with fast diffusion. We prove that the line enhances the asymptotic speed of propagation in a cone of directions. Past the critical angle given by this cone, the asymptotic speed of propagation coincides with the classical Fisher-KPP invasion speed. Several qualitative properties are further derived, such as the limiting behaviour when the diffusion on the line goes to infinity.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Henri Berestycki
    • 1
  • Jean-Michel Roquejoffre
    • 2
  • Luca Rossi
    • 1
  1. 1.Ecole des Hautes Etudes en Sciences SocialesPSL Research UniversityParisFrance
  2. 2.Institut de Mathématiques de ToulouseUniversité Paul SabatierToulouse Cedex 4France

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