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Stochastic and variational approach to finite difference approximation of Hamilton-Jacobi equations and its application
时间  Datetime
2019-12-05 15:30 — 16:30 
地点  Venue
Large Conference Room(706)
报告人  Speaker
Kohei Soga
单位  Affiliation
Keio University
邀请人  Host
Kaizhi WANG
报告摘要  Abstract

Introducing a stochastic and variational formulation, I show that the well-known Lax-Friedrichs type finite difference scheme yields a viscosity solution of Hamilton-Jacobi equations, its derivative and its backward characteristic curves all in once (the results include entropy solutions of scalar conservation laws).  The idea is to treat the discretized equations in terms of optimal control theory, where the so-called numerical viscosity of the difference equations requires controlled random walks. Convergence of the scheme is obtained through the law of large numbers for random walks. As an important application of this framework, I will show numerical methods of weak KAM theory.