报告题目 (Title)： Two-dimensional signal-dependent parabolic-elliptic Keller-Segel system and its mean field derivation (一)
（二维奇性依赖的抛物-椭圆型的Keller-Segel方程和其平均场极限推导）
报告人 (Speaker)： Lukas Bol 博士（曼海姆大学）
报告时间 (Time)：2025年10月30日（周四）10:00
报告地点 (Place)：校本部GJ303
邀请人(Inviter)：盛万成 教授
主办部门：太阳集团官网8722数学系
报告摘要：In this seminar, we will talk about the well-posedness of two-dimensional signal-dependent Keller-Segel system and its mean field derivation from an interacting particle system on the whole space. We start by giving an overview of the topics, which include the existence of sufficiently good solutions, convergence of the particle trajectories in expectation and by using the relative entropy method, the strong convergence for the propagation of chaos. Next, we will rigorously discuss the signal-dependent Keller-Segel system. The signal dependence effect is reflected by the fact that the diffusion coefficient in the particle system depends nonlinearly on the interactions between the individuals. Therefore, the mathematical challenge in studying the well-posedness of this system lies in the possible degeneracy and the aggregation effect when the concentration of signal becomes unbounded. The well-established method on bounded domain, to obtain the appropriate estimates for the signal concentration, is invalid for the whole space case. Motivated by the entropy minimization method and Onofri’s inequality, which has been successfully applied for parabolic-parabolic Keller-Segel system, we establish a complete entropy estimate benefited from linear diffusion term, which plays important role in obtaining the estimates for the solution. Furthermore, the upper bound for the concentration of signal is obtained. We begin to show uniform estimates for the solutions and of the mollified version of the PDE.
