报告人：陈丽 教授（德国曼海姆大学）
报告时间：2025年06月24日上午9：30-10：30
报告地点：维格堂319
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.
报告人简介：陈丽，2001年于吉林大学获博士学位，2001年至2003年于中国科学院数学研究所做博士后，2003年至2013年在清华大学任教；2014年至今任德国曼海姆大学讲座教授，研究方向为偏微分方程及应用。近年来，在反应扩散方程及交叉扩散方程组，多粒子系统的平均场极限，动力学模型，量子力学中的物质稳定性问题等方面做出了多项研究成果，发表在包括SIAM J. Math. Anal.; Comm. Math. Phys.; J. Funct. Anal.; Calc. Var. Partial Differential Equations; J. Differential Equations; Comm. PDE; Proc. Roy. Soc. Edinburgh Sect. A等国际知名数学期刊。
邀请人：王云