The vanishing discount problem for monotone systems of Hamilton-Jacobi equations: part 2-nonlinear coupling
The vanishing discount problem for monotone systems of Hamilton-Jacobi equations: part 2-nonlinear coupling
复制标题
Hamilton-Jacobi 方程单调系统的折扣消失问题：第 2 部分 - 非线性耦合
DOI：
10.1007/s00526-020-01768-8
复制
发表时间：
2020
影响因子：
2.1
通讯作者：
Jin Liang
中科院分区：
文献类型：
--
作者：
Ishii Hitoshi;Jin Liang
研究一类非线性单调Hamilton-Jacobi方程组的消失折扣问题。这继续了第一作者对单调Hamilton-Jacobi方程组的消失折扣问题的研究。与第一部分一样，我们引入了系统的凸对偶Mather测度及其类似测度，分别称为Mather测度和Green-Poisson测度，并证明了消失折扣问题的一个收敛定理。此外，我们建立了遍历问题的存在性结果。
We study the vanishing discount problem for a nonlinear monotone system of Hamilton–Jacobi equations. This continues the first author’s investigation on the vanishing discount problem for a monotone system of Hamilton–Jacobi equations. As in part 1, we introduce by the convex duality Mather measures and their analogues for the system, which we call respectively Mather and Green–Poisson measures, and prove a convergence theorem for the vanishing discount problem. Moreover, we establish an existence result for the ergodic problem.