报告题目：Trajectorial version of the $W_h$-gradient flow for nonlinear Fokker-Planck equations
报告人：柳振鑫
报告人简介：柳振鑫，大连理工大学数学科学bet365手机网址教授。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。
报告内容简介：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
报告时间：2025年11月30日10:30
报告地点：实训楼109
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