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 Benamou and Brenier 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 localizing 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‐) interaction system on the tensor‐weighted Euclidean space.
- Standort
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Deutsche Nationalbibliothek Frankfurt am Main
- Umfang
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Online-Ressource
- Sprache
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Englisch
- Erschienen in
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Graph‐to‐local limit for a multi‐species nonlocal cross‐interaction system ; day:23 ; month:09 ; year:2023 ; extent:8
Proceedings in applied mathematics and mechanics ; (23.09.2023) (gesamt 8)
- Urheber
- DOI
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10.1002/pamm.202300094
- URN
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urn:nbn:de:101:1-2023092415010686451192
- Rechteinformation
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Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Letzte Aktualisierung
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14.08.2025, 10:57 MESZ
Datenpartner
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Beteiligte
- Esposito, Antonio
- Heinze, Georg
- Pietschmann, Jan-Frederik
- Schlichting, André
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