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arXiv · 2306.17414

Graph-to-local limit for a multi-species nonlocal cross-interaction system

Antonio Esposito·Georg Heinze·Jan-Frederik Pietschmann·André Schlichting
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Abstract

In this note we continue the study of nonlocal interaction dynamics on a sequence of infinite graphs, extending the results of [Esposito et. al 2023+] to an arbitrary number of species. Our analysis relies on the observation that the graph dynamics form a gradient flow with respect to a non-symmetric Finslerian gradient structure. Keeping the nonlocal interaction energy fixed, while localising the graph structure, we are able to prove evolutionary Γ-convergence to an Otto-Wassertein-type gradient flow with a tensor-weighted, yet symmetric, inner product. As a byproduct this implies the existence of solutions to the multi-species non-local (cross-)interacation system on the tensor-weighted Euclidean space

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Antonio Esposito, Georg Heinze, Jan-Frederik Pietschmann, André Schlichting. 2023-06-30. Graph-to-local limit for a multi-species nonlocal cross-interaction system. https://arxiv.org/abs/2306.17414

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