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Mathematics > Analysis of PDEs

arXiv:1410.4738 (math)
[Submitted on 17 Oct 2014 (v1), last revised 24 Jun 2015 (this version, v2)]

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

Authors:Laurent Dietrich
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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 an hypoelliptic system, which is shown to admit a travelling wave profile.
Comments: Version 2 (minor corrections)
Subjects: Analysis of PDEs (math.AP)
MSC classes: 35K07, 35C07
Cite as: arXiv:1410.4738 [math.AP]
  (or arXiv:1410.4738v2 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1410.4738
Journal reference: Trans. Amer. Math. Soc. 2015

Submission history

From: Laurent Dietrich [view email]
[v1] Fri, 17 Oct 2014 14:32:46 UTC (68 KB)
[v2] Wed, 24 Jun 2015 16:02:47 UTC (68 KB)
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