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

Author:

Fetecau Razvan C.1,Park Hansol2,Patacchini Francesco S.34

Affiliation:

1. Department of Mathematics, Simon Fraser University, Burnaby, Canada, BC V5A 1S6, Canada

2. Department of Mathematical Sciences, Seoul National University, Seoul 08826, Republic of Korea

3. Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, USA

4. IFP Energies nouvelles, 1-4 avenue de Bois-Préau, 92852 Rueil-Malmaison, France

Abstract

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).

Publisher

World Scientific Pub Co Pte Ltd

Subject

Applied Mathematics,Analysis

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