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

2015/04/18 by Luca Rossi, Rossi, Luca, A. Tellini +3
Computer Science · Mathematics · Medicine · #Advanced Mathematical Modeling in Engineering #Differential Equations and Numerical Methods #Mathematical and Theoretical Epidemiology and Ecology Models

paper · pdf · doi:10.48550/arxiv.1504.04698

Abstract

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

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