报告时间：2026年4月17日（周五）上午 09:45-10:45

报告地点：西汉姆联天赐庄校区精正楼1楼报告厅

报告人：柳振鑫 教授，大连理工大学

报告摘要：

In this talk, we will introduce a trajectorial approach to the gradient flow of nonlinear Fokker-Planck equations. We first give the definitions of the generalized entropy and the modified Wasserstein metric $W_h$, which is adapted to the nonlinear setting. Then we establish the trajectorial version of the relative entropy dissipation identity by McKean-Vlasov SDEs. Averaging the energy dissipation of trajectories yields the free energy dissipation of nonlinear Fokker-Planck equations. Furthermore, leveraging properties of the tangent space of $(\mathcal{P}_2({\mathbb R}^d), W_h)$, we derive the $W_h$-gradient flow. As an illustrative example, we analyze the Fermi-Dirac-Fokker-Planck equation. We conclude with two questions motivated by numerical observations. This talk is based on the collaboration with Xuewei Wang.

报告人简介：

柳振鑫，大连理工大学BW·西汉姆联教授。主要从事随机动力系统的研究，在随机Conley指标理论、随机动力系统中的回复性和稳定性、Kolmogorov平稳分布极限问题、随机平均原理等方面做出系统深入的研究工作。目前已发表学术论文40余篇。2010年获全国百篇优秀博士学位论文提名奖；2015年获得国家优秀青年科学基金资助；2019年获得国家杰出青年科学基金资助。

邀请人：杨大伟