Trajectorial version of the $W_h$-gradient flow for nonlinear Fokker-Planck equations
报告人:柳振鑫
报告地点:腾讯会议ID:197-175-503,密码:260819
报告时间:2026年08月19日星期三19:30-20:30
邀请人:高鹏
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.
主讲人简介:
柳振鑫,大连理工大学数学科学学院教授。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50余篇。2010年获全国百篇优秀博士学位论文提名奖;2015年入选国家级高层次青年人才;2019年入选国家级高层次领军人才。