The shape of expansion induced by a line with fast diffusion in Fisher-KPP equations

Henri Berestycki, Jean-Michel Roquejoffre, Luca Rossi

Published 2014-02-06, updated 2015-01-08Version 2

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.