球面和其他流形上具有本征相互作用的聚集模型的适定性和渐近行为

IF 2 2区数学 Q1 MATHEMATICS

Analysis and Applications Pub Date : 2021-04-19 DOI:10.1142/S0219530521500081

R. Fetecau, Hansol Park, F. Patacchini

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引用次数: 15

摘要

我们研究了黎曼流形上具有内在相互作用的集体行为模型。我们建立了球上测量值解(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，其主要目标是建立共识状态渐近形成的充分条件。对其他流形(如超柱)的解的适定性和一致的形成也进行了研究。

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

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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来源期刊

Analysis and Applications 数学-数学

CiteScore

3.90

自引率

4.50%

发文量

审稿时长

>12 weeks

期刊介绍： Analysis and Applications publishes high quality mathematical papers that treat those parts of analysis which have direct or potential applications to the physical and biological sciences and engineering. Some of the topics from analysis include approximation theory, asymptotic analysis, calculus of variations, integral equations, integral transforms, ordinary and partial differential equations, delay differential equations, and perturbation methods. The primary aim of the journal is to encourage the development of new techniques and results in applied analysis.