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.
- Location
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Deutsche Nationalbibliothek Frankfurt am Main
- Extent
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Online-Ressource
- Language
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Englisch
- Bibliographic citation
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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)
- Creator
- DOI
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10.1002/pamm.202300094
- URN
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urn:nbn:de:101:1-2023092415010686451192
- Rights
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Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Last update
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14.08.2025, 10:57 AM CEST
Data provider
Deutsche Nationalbibliothek. If you have any questions about the object, please contact the data provider.
Associated
- Esposito, Antonio
- Heinze, Georg
- Pietschmann, Jan-Frederik
- Schlichting, André
Other Objects (12)
Graph‐to‐local limit for a multi‐species nonlocal cross‐interaction system
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Introduction [Multispecies futures]
Graph‐to‐local limit for a multi‐species nonlocal cross‐interaction system
Nonlocal-Interaction Equation on Graphs: Gradient Flow Structure and Continuum Limit
Graph-based nonlocal gradient systems and their local limits
On nonlocal minimal graphs
Transmission Efficiency Limit for Nonlocal Metalenses
Multispecies Monocultures.
Multispecies Communities
Sharp interface limit for nonlocal phase field equations
Pattern formation for local/nonlocal interaction functionals
Limits of graph sequences
Epilogue [Multispecies futures]
Introduction [Multispecies futures]
Graph‐to‐local limit for a multi‐species nonlocal cross‐interaction system
Nonlocal-Interaction Equation on Graphs: Gradient Flow Structure and Continuum Limit
Graph-based nonlocal gradient systems and their local limits
On nonlocal minimal graphs
Transmission Efficiency Limit for Nonlocal Metalenses
Multispecies Monocultures.
Multispecies Communities
Sharp interface limit for nonlocal phase field equations
Pattern formation for local/nonlocal interaction functionals
Limits of graph sequences
Epilogue [Multispecies futures]