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Transactions of the American Mathematical Society

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


Author: Laurent Dietrich
Journal: Trans. Amer. Math. Soc. 369 (2017), 3221-3252
MSC (2010): Primary 35H10, 35K57
DOI: https://doi.org/10.1090/tran/6776
Published electronically: September 13, 2016
MathSciNet review: 3605970
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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 a hypoelliptic system, which is shown to admit a travelling wave profile.


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Additional Information

Laurent Dietrich
Affiliation: Institut de Mathématiques de Toulouse, UMR5219, Université de Toulouse, CNRS, UPS IMT, F-31062 Toulouse Cedex 9, France
Address at time of publication: Department of Mathematical Sciences, Carnegie Mellon University, Wean Hall 7115, Pittsburgh, Pennsylvania 15213-3890
Email: ldi@cmu.edu

DOI: https://doi.org/10.1090/tran/6776
Received by editor(s): October 6, 2014
Received by editor(s) in revised form: April 29, 2015
Published electronically: September 13, 2016
Article copyright: © Copyright 2016 American Mathematical Society