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Mathematics in Engineering

2021, Volume 3, Issue 1: 1-16. doi: 10.3934/mine.2021006
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Improved bounds for reaction-diffusion propagation driven by a line of nonlocal diffusion

  • Institut de Mathématiques de Toulouse (UMR CNRS 5219), Université Toulouse ó, 118 route de Narbonne, 31062 Toulouse cedex, France
  • Received: 07 November 2019 Accepted: 29 July 2020 Published: 18 August 2020

  • We consider here a model of accelerating fronts, consisting of one equation with nonlocal diffusion on a line, coupled via the boundary condition with a reaction-diffusion equation of the Fisher-KPP type in the upper half-plane. It was proposed in a previous work by H. Berestycki, L. Rossi and the authors, as a mechanism of front acceleration by a line of fast diffusion. In this latter work, it was indeed proved that the propagation in the direction of the line was exponentially fast in time. Inspired by numerical simulations of the first author, we make the estimate more precise by computing a time algebraic correction.

    Citation: Anne-Charline Chalmin, Jean-Michel Roquejoffre. Improved bounds for reaction-diffusion propagation driven by a line of nonlocal diffusion[J]. Mathematics in Engineering, 2021, 3(1): 1-16. doi: 10.3934/mine.2021006

    Related Papers:

  • We consider here a model of accelerating fronts, consisting of one equation with nonlocal diffusion on a line, coupled via the boundary condition with a reaction-diffusion equation of the Fisher-KPP type in the upper half-plane. It was proposed in a previous work by H. Berestycki, L. Rossi and the authors, as a mechanism of front acceleration by a line of fast diffusion. In this latter work, it was indeed proved that the propagation in the direction of the line was exponentially fast in time. Inspired by numerical simulations of the first author, we make the estimate more precise by computing a time algebraic correction.


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    [10] Coulon Chalmin AC, Fast propagation in reaction-diffusion equations with fractional diffusion, PhD thesis, 2014. Available from: thesesups.ups-tlse.fr/2427/.
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