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arXiv · 2004.06951

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

Razvan C. Fetecau·Hansol Park·Francesco S. Patacchini
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Abstract

We investigate a model for collective behaviour with intrinsic interactions on Riemannian manifolds. We establish the well-posedness of measure solutions (defined via mass transport) on sphere, as well as investigate the mean-field particle approximation. We study the long-time behaviour 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).

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Razvan C. Fetecau, Hansol Park, Francesco S. Patacchini. 2020-04-15. Well-posedness and asymptotic behaviour of an aggregation model with intrinsic interactions on sphere and other manifolds. https://arxiv.org/abs/2004.06951

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