Velocity enhancement of reaction-diffusion fronts by a line of fast diffusion

Dietrich, Laurent

doi:10.1090/tran/6776

Velocity enhancement of reaction-diffusion fronts by a line of fast diffusion
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Trans. Amer. Math. Soc. 369 (2017), 3221-3252 Request permission

Abstract:

We study the velocity of travelling waves of a reaction-diffusion system coupling a standard reaction-diffusion equation in a strip with a one-dimensional diffusion equation on a line. We show that it grows like the square root of the diffusivity on the line. This generalises a result of Berestycki, Roquejoffre and Rossi in the context of Fisher-KPP propagation, where the question could be reduced to algebraic computations. Thus, our work shows that this phenomenon is a robust one. The ratio between the asymptotic velocity and the square root of the diffusivity on the line is characterised as the unique admissible velocity for fronts of a hypoelliptic system, which is shown to admit a travelling wave profile.

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