Graph-to-local limit for the nonlocal interaction equation

2023/06/06 by Antonio Esposito, Georg Heinze, Esposito, Antonio +3 · 2 citations
Mathematics · #Advanced Mathematical Physics Problems #Nonlinear Partial Differential Equations #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2306.03475

Abstract

We study a class of nonlocal partial differential equations presenting a tensor-mobility, in space, obtained asymptotically from nonlocal dynamics on localising infinite graphs. Our strategy relies on the variational structure of both equations, being a Riemannian and Finslerian gradient flow, respectively. More precisely, we prove that weak solutions of the nonlocal interaction equation on graphs converge to weak solutions of the aforementioned class of nonlocal interaction equation with a tensor-mobility in the Euclidean space. This highlights an interesting property of the graph, being a potential space-discretisation for the equation under study.

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• Fokker-Planck equations on discrete infinite graphs
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