报告题目: Mean-Field Control for Diffusion Aggregation system with Coulomb Interaction
报告人：陈丽（曼海姆大学）
邀请人&主持人：黄辉
报告时间与地点：12月4号下午4点， Zoom 会议：925 1960 5714，密码：917091
报告摘要: In this talk, I will represent a recent work on mean-field control problem for a multi-dimensional diffusion-aggregation system with Coulomb interaction (the so called parabolic elliptic Keller-Segel system). The existence of optimal control is proved through the $\Gamma$-convergence of the corresponding control problem of the interacting particle system. There are three building blocks in the whole argument. Firstly, for the optimal control problem on the particle level, instead of using classical method for stochastic system, we study directly the control problem of high-dimensional parabolic equation, i.e. the Liouville equation of it. Secondly, we obtain a strong propagation of chaos result for the interacting particle system by combining the convergence in probability and relative entropy method. Due to this strong mean field limit result, we avoid giving compact support requirement for control functions, which has been often used in the literature. Thirdly, because of strong aggregation effect, additional difficulties arise from control function in obtaining the well-posedness theory of the diffusion-aggregation equation, so that the known method cannot be directly applied. Instead, we use a combination of local existence result and bootstrap argument to obtain the global solution in the sub-critical regime. The talk is based on a joint work with Yucheng Wang and Zhao Wang.
报告人介绍：Li Chen is a professor at the University of Mannheim in Germany and has made outstanding achievements and has profound academic attainments in the field of mathematics. Li Chen obtained her Ph.D. from Jilin University in 2001. From 2001 to 2003, she did post-doctoral research at the Institute of Mathematics, Chinese Academy of Sciences. From 2003 to 2013, she worked at Tsinghua University, and since 2014, she has been a Chair Professor at the University of Mannheim in Germany. Her research direction is partial differential equations and their applications. Her main achievements have been published in many internationally renowned mathematics journals. Professor Chen Li is very active in the academic field. She has presided over several projects funded by the National Natural Science Foundation of China and is currently in charge of three projects funded by the German National Natural Science Foundation. She has also been invited to the United States, Canada, France, Italy, Austria and other countries to participate in academic conferences and give academic reports.
