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arXiv · 2210.10153

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

Razvan C. Fetecau·Hansol Park
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Abstract

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.

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Razvan C. Fetecau, Hansol Park. 2022-10-18. Long-time behaviour of interaction models on Riemannian manifolds with bounded curvature. https://arxiv.org/abs/2210.10153

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