On a class of nonlocal continuity equations on graphs - IFPEN - IFP Energies nouvelles Accéder directement au contenu
Article Dans Une Revue European Journal of Applied Mathematics Année : 2024

On a class of nonlocal continuity equations on graphs

Résumé

Motivated by applications in data science, we study partial differential equations on graphs. By a classical fixed-point argument, we show existence and uniqueness of solutions to a class of nonlocal continuity equations on graphs. We consider general interpolation functions, which give rise to a variety of different dynamics, for example, the nonlocal interaction dynamics coming from a solution-dependent velocity field. Our analysis reveals structural differences with the more standard Euclidean space, as some analogous properties rely on the interpolation chosen.
Fichier principal
Vignette du fichier
on-a-class-of-nonlocal-continuity-equations-on-graphs.pdf (255.02 Ko) Télécharger le fichier
Origine : Publication financée par une institution
Licence : CC BY - Paternité

Dates et versions

hal-04501709 , version 1 (14-03-2024)

Licence

Paternité

Identifiants

Citer

Antonio Esposito, Francesco Saverio Patacchini, André Schlichting. On a class of nonlocal continuity equations on graphs. European Journal of Applied Mathematics, 2024, 35 (1), pp.109-126. ⟨10.1017/S0956792523000128⟩. ⟨hal-04501709⟩

Collections

IFP TDS-MACS
14 Consultations
3 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More