On a Hamilton-Jacobi theory for Hydrodynamic limit of action minimizing collective dynamics
数学专题报告
报告题目(Title)：On a Hamilton-Jacobi theory for Hydrodynamic limit of action minimizing collective dynamics
报告人(Speaker)：Jin Feng (University of Kansas)
地点(Place)：后主楼1124
时间(Time)：2025 年 6月 17日 下午16:00-17:00
邀请人(Inviter)：苏喜锋
报告摘要
We examine a class of multi-scale limit theorems for Hamilton-Jacobi equations defined in space of probability measures. They correspond to first principle hydrodynamic limit derivations on certain aspects of continuum level conservation law equations. We rely upon versions of abstract viscosity solution, as well as variational arguments, to study problems about (global) action minimizing collective Hamiltonian dynamics.
Our tools are mainly mass transport calculus, finite dimensional weak KAM (Kolmogorov- Arnold-Moser) theory, and viscosity solution theory for Hamilton-Jacobi equations in space of probability measures (studied using first order calculus in Alexandrov metric spaces). This is a joint work with Toshio Mikami.
