主 题: A Hamilton-Jacobi theory for the hydrodynamic limit large deviation of nonlinear heat equation from stochastic Carleman particles
报告人: Professor Jin Feng (University of Kansas)
时 间: 2018-07-03 09:30-10:30
地 点: Room 1418, Sciences Building No. 1
Abstract: The deterministic Carleman equation can be considered as an one dimensional two speed fictitious gas model. Its associated hydrodynamic limit gives a nonlinear heat equation. The rigorous derivation of such limit was known since the 1970th. In this talk, starting from a more refined stochastic model giving the Carleman equation as the mean field, we derive a fluctuation structure associated with the hydrodynamic limit.
The large deviation result is established through an abstract Hamilton-Jacobi method by Kurtz and myself applied to this specific setting. The principal idea is to identify a two scale averaging structure in the context of Hamiltonian convergence in the space of probability measures. This is achieved through a change of coordinate to the density-flux description of the problem. We also extend a method in the weak KAM theory to the infinite particle context for explicitly identifying the effective Hamiltonian. In the end, we conclude by establishing a comparison principle for a set of Hamilton-Jacobi equation in the space of measures.
At the present time, there is still a gap in the rigorous development between what we want and what we have. Time permitting, II will present some subtle issues involved and also put the method in perspective regarding challenges we face when applying the method to other hydrodynamic limit issues.
This is a joint work with Toshio Mikami and Johannes Zimmer.