arXiv:2210.10153 Abstract | arXiv Analytics

arXiv:2210.10153 [math.AP]Abstract References Reviews Resources

Long-time behaviour of interaction models on Riemannian manifolds with bounded curvature

Published 2022-10-18Version 1

We investigate the long-time behaviour of solutions to a nonlocal partial differential equation on smooth Riemannian manifolds of bounded sectional curvature. The equation models self-collective behaviour with intrinsic interactions that are modelled by an interaction potential. We consider attractive interaction potentials and establish sufficient conditions for a consensus state to form asymptotically. In addition, we quantify the approach to consensus, by deriving a convergence rate for the diameter of the solution's support. The analytical results are supported by numerical simulations for the equation set up on the rotation group.

Categories: math.AP, math.DG

Subjects: 35A30, 35B38, 35B40, 58J90

Keywords: long-time behaviour, interaction models, bounded curvature, interaction potential, nonlocal partial differential equation

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