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Mean-Field Control for Diffusion Aggregation system with Coulomb Interaction
时间:2025年08月16日 19:03 点击数:

报告人:陈丽

报告地点:数学与统计学院619

报告时间:2025年08月20日星期三10:00-11:00

邀请人:张凯军、李敬宇

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.

主讲人简介:

2001年获吉林大学博士学位,2001年至2003年于中国科学院数学研究所跟随肖玲老师做博士后,2003年至2013年于清华大学任教,2014年至今任德国Mannheim大学讲座教授。研究方向为偏微分方程及应用。近年来,在反应扩散方程,多粒子系统的平均场极限,动力学模型等方面做出了众多成果,论文发表在SIMA, CMP, JFA., CVPDE, JDE, CPDE 等国际知名数学期刊上。

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