Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	Jin Feng教授，Department of Mathematics，University of Kansas, U.S.A.
Inviter:
Title:	Derivation of a nonlinear heat equation and its macroscopic fluctuation structures from Carleman particle models——A Hamilton-Jacobi approach
Time & Venue:	2021.06.25 10:00-11:00 腾讯会议：544273444 密码：123456
Abstract:	The deterministic Carleman equation can be considered as a one dimensional two speed fictitious gas model. Its associated (2 scale) hydrodynamic limit gives a nonlinear heat equation. The first rigorous derivation of such limit was given by Kurtz in 1973. In this talk, starting from a particle level Lagrangian structure giving the Carleman equation as zero cost curves at a mean field limit, we derive a macroscopic fluctuation (Hamiltonian and Lagrangian) structure at the next hydrodynamic limit (i.e. 2-scale) level. The first part of the talk is aimed at explaining everything deterministically using variational analysis and Hamilton-Jacobi theory in the space of probability measures, the second part will connect to probability theory of large deviation and give the background construct of the Lagrangian structure that we give matter-of-factly in beginning of the talk. This is a joint work with Toshio Mikami and Johannes Zimmer.