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科学研究
RESEARCH
Nonlinear generalizations of the vanishing discount problem
时间  Datetime
2020-11-24 14:30 — 15:30
地点  Venue
腾讯会议 APP3()
报告人  Speaker
陈秦波
单位  Affiliation
KTH Royal Institute of Technology
邀请人  Host
王楷植
备注  remarks
会议 ID:557 635 661 会议密码:123123
报告摘要  Abstract

We will generalize the vanishing discount problem (also known as ergodic approximation) to those Hamiltonians depending nonlinearly on the unknown function. Let H(x, p, u) be a continuous Hamiltonian which is strictly increasing in u, and is convex and coercive in p. For each small parameter λ>0, let uλ denote the unique viscosity solution of the H-J equation H(x, Du(x), λ u(x))=c, we are then interested in the asymptotic behavior of the whole family of solutions {uλ}. In this talk, I will present a convergence result and explain how to characterize the limit solution. The method is based on the non-smooth Aubry-Mather theory.