Graph-to-local limit for a multi-species nonlocal cross-interaction system
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 {\Gamma}-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
Cite
@article{arxiv.2306.17414,
title = {Graph-to-local limit for a multi-species nonlocal cross-interaction system},
author = {Antonio Esposito and Georg Heinze and Jan-Frederik Pietschmann and André Schlichting},
journal= {arXiv preprint arXiv:2306.17414},
year = {2023}
}
Comments
arXiv admin note: text overlap with arXiv:2306.03475