Propagation reversal on trees in the large diffusion regime

arXiv (Cornell University)

Abstract

In this work we study travelling wave solutions to bistable reaction diffusion equations on bi-infinite $k$-ary trees in the continuum regime where the diffusion parameter is large. Adapting the spectral convergence method developed by Bates and his coworkers, we find an asymptotic prediction for the speed of travelling front solutions. In addition, we prove that the associated profiles converge to the solutions of a suitable limiting reaction-diffusion PDE. Finally, for the standard cubic nonlinearity we provide explicit formula's to bound the thin region in parameter space where the propagation direction undergoes a reversal.

Authors 2

1. Hermen Jan Hupkes Aachen Mathematisch Instituut

   Leiden University

   Affiliation as printed

   Mathematisch Instituut , Universiteit Leiden , P.O. Box 9512 , 2300 RA Leiden , The Netherlands

2. Mia Jukić Aachen Mathematisch Instituut

   Leiden University · Netherlands Organisation for Applied Scientific Research

   Affiliation as printed

   Electromagnetic Signatures & Propagation , Netherlands Organisation for Applied Scientific Research (TNO) , 2509 JG The Hague , The Netherlands

   Mathematisch Instituut , Universiteit Leiden , P.O. Box 9512 , 2300 RA Leiden , The Netherlands