Generalized ergodic problems: existence and uniqueness structures of solutions

Autor: Jing, Wenjia, Mitake, Hiroyoshi, Tran, Hung V.
Rok vydání: 2019
Předmět:
Druh dokumentu: Working Paper
Popis: 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.
Comment: 21 pages
Databáze: arXiv