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arXiv · 1402.1441

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

Henri Berestycki·Jean-Michel Roquejoffre·Luca Rossi
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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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Henri Berestycki, Jean-Michel Roquejoffre, Luca Rossi. 2014-02-06. The shape of expansion induced by a line with fast diffusion in Fisher-KPP equations. https://arxiv.org/abs/1402.1441

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