Generalized ergodic problems: Existence and uniqueness structures of solutions

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:268

Article

Jing, Wenjia¹  Mitake, Hiroyoshi²  Tran, Hung V.³ 

[1] Tsinghua Univ, Yau Math Sci Ctr, 1 Tsinghua Yuan, Beijing 100084, Peoples R China

[2] Univ Tokyo, Grad Sch Math Sci, Meguro Ku, 3-8-1 Komaba, Tokyo 1538914, Japan

[3] Univ Wisconsin, Dept Math, Van Vleck Hall,480 Lincoln Dr, Madison, WI 53706 USA

关键词: Generalized ergodic problems;    Contact Hamilton-Jacobi equations;    Nonlinear adjoint method;    Nonuniqueness of solutions;    Uniqueness structures;    Viscosity solutions;   

DOI  :  10.1016/j.jde.2019.09.046

来源: Elsevier

【 摘 要 】

We study a generalized ergodic problem (E), which is a Hamilton-Jacobi equation of contact type, in the flat n-dimensional torus. We first obtain existence of solutions to this problem under quite general assumptions. Various examples are presented and analyzed to show that (E) does not have unique solutions in general. We then study uniqueness structures of solutions to (E) in the convex setting by using the nonlinear adjoint method. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free