報告時間：2024年10月23日 （周三）15:30-16:30
報告地點：騰訊會議（線上） 會議ID:211180675
邀請人：國家級教學名師朱傳喜教授
報告摘要：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.
報告人簡介：薛小平，哈爾濱工業大學伟德bv，教授，博士生導師。美國《數學評論》評論員，曾任中國數學會理事，現任中國系統工程學會模糊系統與模糊數學專業委員會副主任，黑龍江省數學會理事長，黑龍江省傑出青年基金獲得者。主要研究領域為：無窮維優化與變分、神經網絡優化與控制、微分包含與動力系統分析、模糊數學等。主持國家自然科學基金面上項目5項，出版教材與專著5部，獲省部級二等獎3項，發表SCI學術論文100餘篇，涉及相關領域期刊50餘種，其中包括代表應用數學最高水平的SIAM列雜志，微分方程、控制領域權威期刊，工程領域IEEE系列彙刊等。