球面和其他流形上具有内禀相互作用的凝聚模型的适定性和渐近性
Well-posedness and asymptotic behaviour of an aggregation model with intrinsic interactions on sphere and other manifolds
摘要：
本文研究了黎曼流形上具有内禀相互作用的集体行为模型。我们建立了球上测度解（通过质量输运定义）的适定性，并研究了平均场粒子近似。我们研究了球面上模型解的长时间行为，主要目的是建立一致状态渐近形成的充分条件。解的适定性和共识的形成也被研究用于其他流形（例如，超圆柱体）。
英文摘要：
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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