On evolution PDEs on co-evolving graphs
We provide a well-posedness theory for a class of nonlocal continuity equations on co-evolving graphs. We describe the connection among vertices through an edge weight function and we let it evolve in time, coupling its dynamics with the dynamics on the graph. This is relevant in applications to opi...
| Главные авторы: | , |
|---|---|
| Формат: | Journal article |
| Язык: | English |
| Опубликовано: |
American Institute of Mathematical Sciences
2024
|
| _version_ | 1826314596618600448 |
|---|---|
| author | Esposito, A Mikolás, L |
| author_facet | Esposito, A Mikolás, L |
| author_sort | Esposito, A |
| collection | OXFORD |
| description | We provide a well-posedness theory for a class of nonlocal continuity equations on co-evolving graphs. We describe the connection among vertices through an edge weight function and we let it evolve in time, coupling its dynamics with the dynamics on the graph. This is relevant in applications to opinion dynamics and transportation networks. Existence and uniqueness of suitably defined solutions is obtained by exploiting the Banach fixed-point theorem. We consider different time scales for the evolution of the weight function: faster and slower than the flow defined on the graph. The former leads to graphs whose weight functions depend nonlocally on the density configuration at the vertices, while the latter induces static graphs. Furthermore, we prove a discrete-to-continuum limit for the PDEs under study as the number of vertices converges to infinity. |
| first_indexed | 2024-04-09T03:57:45Z |
| format | Journal article |
| id | oxford-uuid:57bd2672-c1ae-4f72-b2f7-6ebff8a46079 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-09-25T04:36:11Z |
| publishDate | 2024 |
| publisher | American Institute of Mathematical Sciences |
| record_format | dspace |
| spelling | oxford-uuid:57bd2672-c1ae-4f72-b2f7-6ebff8a460792024-09-24T09:34:36ZOn evolution PDEs on co-evolving graphsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:57bd2672-c1ae-4f72-b2f7-6ebff8a46079EnglishSymplectic ElementsAmerican Institute of Mathematical Sciences2024Esposito, AMikolás, LWe provide a well-posedness theory for a class of nonlocal continuity equations on co-evolving graphs. We describe the connection among vertices through an edge weight function and we let it evolve in time, coupling its dynamics with the dynamics on the graph. This is relevant in applications to opinion dynamics and transportation networks. Existence and uniqueness of suitably defined solutions is obtained by exploiting the Banach fixed-point theorem. We consider different time scales for the evolution of the weight function: faster and slower than the flow defined on the graph. The former leads to graphs whose weight functions depend nonlocally on the density configuration at the vertices, while the latter induces static graphs. Furthermore, we prove a discrete-to-continuum limit for the PDEs under study as the number of vertices converges to infinity. |
| spellingShingle | Esposito, A Mikolás, L On evolution PDEs on co-evolving graphs |
| title | On evolution PDEs on co-evolving graphs |
| title_full | On evolution PDEs on co-evolving graphs |
| title_fullStr | On evolution PDEs on co-evolving graphs |
| title_full_unstemmed | On evolution PDEs on co-evolving graphs |
| title_short | On evolution PDEs on co-evolving graphs |
| title_sort | on evolution pdes on co evolving graphs |
| work_keys_str_mv | AT espositoa onevolutionpdesoncoevolvinggraphs AT mikolasl onevolutionpdesoncoevolvinggraphs |