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

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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Correspondence to Henri Berestycki.

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Communicated by L. Caffarelli

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Berestycki, H., Roquejoffre, J. & Rossi, L. The Shape of Expansion Induced by a Line with Fast Diffusion in Fisher-KPP Equations. Commun. Math. Phys. 343, 207–232 (2016). https://doi.org/10.1007/s00220-015-2517-3

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Keywords

  • Critical Angle
  • Comparison Principle
  • Fast Diffusion
  • Spreading Velocity
  • Spreading Speed