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Generalized ergodic problems: Existence and uniqueness structures of solutions
Journal of Differential Equations ( IF 2.4 ) Pub Date : 2020-03-01 , DOI: 10.1016/j.jde.2019.09.046
Wenjia Jing , Hiroyoshi Mitake , Hung V. Tran

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.

中文翻译:

广义遍历问题:解的存在唯一性结构

我们研究了一个广义遍历问题 (E),它是一个接触类型的 Hamilton-Jacobi 方程,在平面 $n$ 维圆环中。我们首先在相当普遍的假设下获得这个问题的解的存在性。提供并分析了各种示例以表明(E)一般没有唯一的解决方案。然后,我们通过使用非线性伴随方法研究凸设置中(E)解的唯一性结构。
更新日期:2020-03-01
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