Generalized ergodic problems: existence and uniqueness structures of solutions
Analysis of PDEs
2019-02-14 v1
Abstract
We study a generalized ergodic problem (E), which is a Hamilton-Jacobi equation of contact type, in the flat -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.
Cite
@article{arxiv.1902.05034,
title = {Generalized ergodic problems: existence and uniqueness structures of solutions},
author = {Wenjia Jing and Hiroyoshi Mitake and Hung V. Tran},
journal= {arXiv preprint arXiv:1902.05034},
year = {2019}
}
Comments
21 pages