Well-posedness and asymptotic behavior of an aggregation model with intrinsic interactions on sphere and other manifolds

Razvan Fetecau (1) , Hansol Park (2) , Francesco Patacchini (3, 4)

1 SFU.ca - Simon Fraser University = Université Simon Fraser
2 SNU - Seoul National University [Seoul]
3 Carnegie Mellon - Department of Mathematical Sciences
4 IFPEN - IFP Energies nouvelles

We investigate a model for collective behavior with intrinsic interactions on Riemannian manifolds. We establish the well-posedness of measure-valued solutions (defined via mass transport) on sphere, as well as investigate the mean-field particle approximation. We study the long-time behavior of solutions to the model on sphere, where the primary goal is to establish sufficient conditions for a consensus state to form asymptotically. Well-posedness of solutions and the formation of consensus are also investigated for other manifolds (e.g., a hypercylinder).

Mots clés: Asymptotic consensus; intrinsic interactions; measure-valued solutions; particle methods; swarming on manifolds

Domaines: Mathématiques [math]

Razvan Fetecau, Hansol Park, Francesco Patacchini. Well-posedness and asymptotic behavior of an aggregation model with intrinsic interactions on sphere and other manifolds. Analysis and Applications, 2021, 19 (06), pp.965-1017. ⟨10.1142/S0219530521500081⟩. ⟨hal-03598029⟩