学术报告

题      目：Large deviation principle and global energy landscape for non-equilibrium chemical reactions

报  告  人：高源   助理教授  (邀请人：袁源 )

                                     普渡大学（Purdue University）

时      间：5月22日  10：00-11：00

地     点：数科院西楼111报告厅

报告人简介:

       Yuan Gao is an assistant professor at the Department of Mathematics, Purdue University. Before joining Purdue in 2021, she was a William W. Elliott Assistant Research Professor at Duke University during 2019-2021. She received her PhD from Fudan University in 2017. Yuan Gao specializes in calculus of variation and numerical analysis for singular nonlinear PDEs rising from crystalline materials, image sciences and microfluids. Her recent research interests are optimal control and Hamilton-Jacobi equations with applications in dynamic system, transition path theory and non-equilibrium chemical reactions.

摘      要：

       Non-equilibrium chemical reactions can be modeled by random time changed Poisson process on countable states. The concentration of each species, defined as the molecular number over the size V of the container, can be then regarded as a continuous time Markov chain. The WKB reformulation for the backward equation is Varadhan's discrete nonlinear semigroup and is also a monotone scheme which approximates the limiting first order Hamiltonian-Jacobi equations(HJE). The discrete Hamiltonian is a m-accretive operator, which generates a nonlinear semigroup on countable grids and justifies the well posedness of chemical master equation. The convergence from the monotone schemes to the viscosity solution of HJE is proved via constructing barriers to overcome the polynomial growth coefficient in Hamiltonian. This convergence of Varadhan's discrete nonlinear semigroup to the continuous Lax-Oleinik semigroup yields the large deviation principle for the chemical reaction process at any single time. Consequently, the macroscopic mean-field limit reaction rate equation is recovered. Moreover, the LDP for invariant measures can be used to construct the global energy landscape for non-equilibrium reactions. It is also proved to be a selected unique weak KAM solution to the corresponding stationary HJE.