2024/12/27 by Petr Stehlík, Stehlík, Petr
Mathematics · Physics and Astronomy · #34A33 #37L60 #39A12 #65M22 #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #Dynamical Systems (math.DS) #FOS: Mathematics #Numerical methods for differential equations #Opinion Dynamics and Social Influence
paper · pdf · doi:10.48550/arxiv.2412.19548
openalex publication_date 2024/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we provide explicit description of the pinning region and propagation reversal phenomenon for the bistable reaction diffusion equation on regular biinfinite trees. In contrast to the general existence results for smooth bistabilities, the closed-form formulas are enabled by the choice of the piecewise linear McKean's caricature. We construct exact pinned waves and show their stability. The results are qualitatively similar to the propagation reversal results for smooth bistabilities. Major exception consists in the unboundedness of the pinning region in the case of the bistable McKean's caricature. Consequently, the propagation reversal also occurs for arbitrarily large diffusion.