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

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).
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Submitted on : Wednesday, March 16, 2022 - 6:56:17 PM
Last modification on : Thursday, March 17, 2022 - 10:53:02 AM

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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, World Scientific Publishing, 2021, 19 (06), pp.965-1017. ⟨10.1142/S0219530521500081⟩. ⟨hal-03598029⟩

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