Nonlocal cross-interaction systems on graphs: Nonquadratic Finslerian structure and nonlinear mobilities

2021/07/23 by Georg Heinze, Heinze, Georg, Jan‐Frederik Pietschmann +3 · 1 citation
Mathematics · Physics and Astronomy · #28A33 #45G10 #45G15 #49J40 #49J45 #Advanced Differential Geometry Research #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2107.11289

openalex publication_date 2021/07/23 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

We study the evolution of a system of two species with nonlinear mobility and nonlocal interactions on a graph whose vertices are given by an arbitrary, positive measure. To this end, we extend a recently introduced 2-Wasserstein-type quasi-metric on generalized graphs, which is based on an upwind-interpolation, to the case of two-species systems, concave, nonlinear mobilities, and p≠ 2. We provide a rigorous interpretation of the interaction system as a gradient flow in the Finslerian setting, arising from the new quasi-metric.

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