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Generalized ergodic problems: Existence and uniqueness structures of solutions

Wenjia Jing Yau Mathematical Sciences Center, Tsinghua University, No.1 Tsinghua Yuan, Beijing 100084, China Hiroyoshi Mitake Graduate School of Mathematical Sciences, University of Tokyo 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8914, Japan Hung V. Tran Department of Mathematics, University of Wisconsin Madison, Van Vleck hall, 480 Lincoln drive, Madison, WI 53706, USA

Analysis of PDEs mathscidoc:2206.03015

Journal of Differential Equations, 268, (6), 2886-2909, 2020.3
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.
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@inproceedings{wenjia2020generalized,
  title={Generalized ergodic problems: Existence and uniqueness structures of solutions},
  author={Wenjia Jing, Hiroyoshi Mitake, and Hung V. Tran},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220626170133418666469},
  booktitle={Journal of Differential Equations},
  volume={268},
  number={6},
  pages={2886-2909},
  year={2020},
}
Wenjia Jing, Hiroyoshi Mitake, and Hung V. Tran. Generalized ergodic problems: Existence and uniqueness structures of solutions. 2020. Vol. 268. In Journal of Differential Equations. pp.2886-2909. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220626170133418666469.
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