WIAS Preprint No. 2103, (2015)

The effect on Fisher--KPP propagation in a cylinder with fast diffusion on the boundary



Authors

  • Rossi, Luca
  • Tellini, Andrea
  • Valdinoci, Enrico
    ORCID: 0000-0001-6222-2272

2010 Mathematics Subject Classification

  • 35K57 35B40 35K40 35B53

Keywords

  • KPP equations, reaction-diffusion systems, different spatial dimensions, asymptotic speed of spreading

Abstract

In this paper we consider a reaction-diffusion equation of Fisher-KPP type inside an infinite cylindrical domain in $R^N+1$, coupled with a reaction-diffusion equation on the boundary of the domain, where potentially fast diffusion is allowed. We will study the existence of an asymptotic speed of propagation for solutions of the Cauchy problem associated with such system, as well as the dependence of this speed on the diffusivity at the boundary and the amplitude of the cylinder. When $N=1$ the domain reduces to a strip between two straight lines. This models the effect of two roads with fast diffusion on a strip-shaped field bounded by them.

Appeared in

  • SIAM J. Math. Anal., 49 (2017), pp. 4595-4624.

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