题目：Fokker-Planck Equations of Neuron Networks：Umerical Simulation and Dilating the Blowup Solution

报告人：周珍楠 副教授 （西湖大学）

地点：致远楼108室

时间：2024年10月31日 16:30-17:30

摘要：In this talk, we are concerned with the Fokker-Planck equations associated with the Nonlinear Noisy Leaky Integrate-and-Fire model for neuron networks. Due to the jump mechanism at the microscopic level, such Fokker-Planck equations are endowed with an unconventional structure: transporting the boundary flux to a specific interior point. In the first part of the talk, we present a conservative and positivity preserving scheme for these Fokker-Planck equations, and we show that in the linear case, the semi-discrete scheme satisfies the discrete relative entropy estimate, which essentially matches the only known long time asymptotic solution property. We also provide extensive numerical tests to verify the scheme properties, and carry out several sets of numerical experiments, including finite-time blowup, convergence to equilibrium and capturing time-period solutions of the variant models. Secondly, we introduce a new notion of genealized solutions for this model with a dynamical time rescaling, so that the extension of solutions after blowups becomes possible.

报告人简介：周珍楠，西湖大学副教授。2014 年在美国威斯康辛大学麦迪逊分校获得博士学位，2014-2017 年在美国杜克大学担任助理研究教授，2017 年加入北京大学北京国际数学研究中心担任助理教授，2024年加入西湖大学理论科学研究院和交叉科学中心。主要研究领域为微分方程的应用分析，微分方程数值解，应用随机分析，随机模拟等，特别是关注来源于自然科学的应用数学问题。

欢迎各位参加！