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

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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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Authors and Affiliations

  1. Ecole des Hautes Etudes en Sciences Sociales, PSL Research University, CNRS, CAMS, 190-198 avenue de France, 75013, Paris, France

    Henri Berestycki & Luca Rossi

  2. Institut de Mathématiques de Toulouse, Université Paul Sabatier, 118 route de Narbonne, 31062, Toulouse Cedex 4, France

    Jean-Michel Roquejoffre

Authors
  1. Henri Berestycki
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  2. Jean-Michel Roquejoffre
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  3. Luca Rossi
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Correspondence to Henri Berestycki.

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Communicated by L. Caffarelli

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Berestycki, H., Roquejoffre, JM. & 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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  • DOI: https://doi.org/10.1007/s00220-015-2517-3

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