Comparison Among Several Planar Fisher-KPP Road-Field Systems

  • Andrea TelliniEmail author
Part of the Springer INdAM Series book series (SINDAMS, volume 33)


In this chapter we consider several reaction-diffusion systems—known as road-field systems—which describe the effect that one (or two) line(s) with heterogeneous diffusion has (have) on the speed of propagation in a planar domain, where the classical Fisher-KPP equation is considered. We recall the results by Berestycki et al. (J. Math. Biol. 66:743–766, 2013) for the case of a line in a half-plane, and those obtained in collaboration with Rossi et al. (SIAM J. Math. Anal. 49, 4595–4624, 2017) for two lines bounding a strip. The main goal is to compare the speed of propagation in the direction of the line(s) of these situations with the cases of a plane with one and two lines on which the diffusion is different with respect to the rest of the planar domain.


Reaction-diffusion systems Asymptotic speed of propagation Diffusion heterogeneities KPP systems Different spatial dimensions 



This work has been supported by the Spanish Ministry of Economy, Industry and Competitiveness through contract Juan de la Cierva Incorporación IJCI-2015-25084 and project MTM2015-65899-P, and by the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013)/ERC Grant Agreement n.321186—ReaDi “Reaction-Diffusion Equations, Propagation and Modelling”.

The author wishes to thank the anonymous referee for his/her comments which have improved the presentation of the results of this work.


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Authors and Affiliations

  1. 1.Universidad Politécnica de MadridETSIDI, Departamento de Matemática Aplicada a la Ingeniería IndustrialMadridSpain

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