Topic: Mean-Field Control for Diffusion Aggregation system with Coulomb Interaction

Lecturer: Chen Li, Professor at the University of Mannheim

Time: Thursday, June 25, 2026, 14:30, UTC+8

Venue: Room 208, Mathematics and Statistics Building

Biography: Prof. Chen Li obtained her Ph.D. from Jilin University in 2001. She worked at Tsinghua University from 2003 to 2013 and has been a Chair Professor at the University of Mannheim in Germany since 2014. Her research focuses on partial differential equations and their applications, with specific interests in reaction-diffusion and cross-diffusion systems, mean-field limits and kinetic models of many-particle systems, and stability problems of matter in quantum mechanics. She has published over 80 SCI-indexed papers in journals such as ARMA, CMP, Trans. Amer. Math. Soc., and Comm. Partial Differential Equations. She has been invited to deliver more than 20 academic reports at conferences in the United States, Canada, France, Italy, Austria, and other countries.

Abstract: In this talk, I will present 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 Γ-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.

Rewritten by: Xu Hanyue

Edited by: Mei Mengqi, Li Tiantian

Source: School of Mathematics and Statistics