Well-posedness of an interaction model on Riemannian manifolds - Archive ouverte HAL Access content directly
Journal Articles Communications on Pure and Applied Analysis Year : 2022

Well-posedness of an interaction model on Riemannian manifolds

(1) , (2)
1
2

Abstract

We investigate a model for collective behaviour with intrinsic interactions on smooth Riemannian manifolds. For regular interaction potentials, we establish the local well-posedness of measure-valued solutions defined via optimal mass transport. We also extend our result to the global well-posedness of solutions for manifolds with nonpositive bounded sectional curvature. The core concept underlying the proofs is that of Lipschitz continuous vector fields in the sense of parallel transport.
Fichier principal
Vignette du fichier
Well posedness of an interaction model on riemannian manifolds.pdf (530.76 Ko) Télécharger le fichier
Origin : Publication funded by an institution

Dates and versions

hal-03877707 , version 1 (06-12-2022)

Licence

Attribution - NonCommercial - NoDerivatives - CC BY 4.0

Identifiers

Cite

Razvan C. Fetecau, Francesco S. Patacchini. Well-posedness of an interaction model on Riemannian manifolds. Communications on Pure and Applied Analysis, 2022, 21 (11), pp.3559-3585. ⟨10.3934/cpaa.2022114⟩. ⟨hal-03877707⟩

Collections

IFP INSMI
0 View
0 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More