论文标题
聚集模型的适应性良好和渐近行为在球体和其他歧管上具有内在相互作用
Well-posedness and asymptotic behaviour of an aggregation model with intrinsic interactions on sphere and other manifolds
论文作者
论文摘要
我们研究了一个模型的集体行为模型，并在里曼尼亚语流形上进行了内在相互作用。我们在球体上建立了测量溶液（通过质量传输定义）的适当性，并研究了平均场粒子近似。我们研究了在球体上的模型解决方案的长期行为，在该模型中，主要目标是建立足够的条件，以使共识状态渐近地形成。还研究了其他歧管（例如，高餐机）的解决方案和共识的形成。
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).
