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 BerestyckiEmail author
  • Jean-Michel Roquejoffre
  • Luca Rossi


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.


Critical Angle Comparison Principle Fast Diffusion Spreading Velocity Spreading Speed 
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© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Henri Berestycki
    • 1
    Email author
  • 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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