Propagation reversal on trees in the large diffusion regime

2024/01/23 by Hermen Jan Hupkes, Hupkes, Hermen Jan, Mia Jukić +1
Computer Science · Mathematics · Medicine · #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Dynamics and Pattern Formation #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2401.12899

openalex publication_date 2024/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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