报告时间：2024年10月23日 （周三）15:30-16:30
报告地点：腾讯会议（线上） 会议ID:211180675
邀请人：国家级教学名师朱传喜教授
报告摘要：We introduce the collective behavior of the infinite-particle Cucker-Smale model with discrete form and kinetic form respectively. For discrete form C-S model, we first establish the boundness of velocity by showing the non-increase of the supremum norm of velocity through classifying the particles according to the norm of velocity, and then obtain the flocking behavior of infinite-particle Cucker-Smale model. More precisely, the solutions will concentrate exponentially fast in velocity to the average of the initial velocity, while in space the position differences between particles will be uniformly bounded. While for the kinetic form C-S model, we focus on the formation behavior of the kinetic C-S model with initial datum not compactly supported in position field. First, we obtain the existence and uniqueness of the classical solutions to the kinetic C-S model by standard approximation method. Second, by using the characteristic flow, we overcome the difficulty of weakening the attraction between particles caused by the non-compact position support through some estimates and establish the formation behavior of the classical solutions to the kinetic Cucker-Smale model, which means the consensus of velocity. Finally, for the measure-valued solutions to the kinetic Cucker-Smale model, the formation behavior is also established.
报告人简介：薛小平，哈尔滨工业大学数学学院，教授，博士生导师。美国《数学评论》评论员，曾任中国数学会理事，现任中国系统工程学会模糊系统与模糊数学专业委员会副主任，黑龙江省数学会理事长，黑龙江省杰出青年基金获得者。主要研究领域为：无穷维优化与变分、神经网络优化与控制、微分包含与动力系统分析、模糊数学等。主持国家自然科学基金面上项目5项，出版教材与专著5部，获省部级二等奖3项，发表SCI学术论文100余篇，涉及相关领域期刊50余种，其中包括代表应用数学最高水平的SIAM列杂志，微分方程、控制领域权威期刊，工程领域IEEE系列汇刊等。