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arXiv · 1111.0408

Transition between linear and exponential propagation in Fisher-KPP type reaction-diffusion equations

Anne-Charline Coulon·Jean-Michel Roquejoffre
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Abstract

We study the Fisher-KPP equation with a fractional laplacian of order {\alpha} \in (0, 1). We know that the stable state invades the unstable one at constant speed for {\alpha} = 1, and at an exponential in time velocity for {\alpha} \in (0, 1). The transition between these two different speeds is examined in this paper. We prove that during a time of the order - ln(1 - {\alpha}), the propagation is linear and then it is exponential.

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Anne-Charline Coulon, Jean-Michel Roquejoffre. 2011-11-02. Transition between linear and exponential propagation in Fisher-KPP type reaction-diffusion equations. https://arxiv.org/abs/1111.0408

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