一个涉及 Hamilton-Jacobi 方程定义域奇异扰动的问题
偏微分方程分析
2017-08-31 v2
摘要
我们研究二维欧几里得空间开子集上 Hamilton-Jacobi 方程的奇异扰动，其中该子集由 Hamilton 函数确定，且 Hamilton-Jacobi 方程是 Hamilton 流的 Hamilton 最优控制的动态规划方程。我们建立了 Hamilton-Jacobi 方程解的收敛性，并将解的极限识别为图上常微分方程组的解。该扰动是奇异的，意指在极限过程中定义域退化为图。从最优控制的角度来看，我们的结果可视为对 Hamilton 流的扰动分析。
引用
@article{arxiv.1607.02224,
title = {A perturbation problem involving singular perturbations of domains for Hamilton-Jacobi equations},
author = {Taiga Kumagai},
journal= {arXiv preprint arXiv:1607.02224},
year = {2017}
}
备注
Portions of this work were developed as arXiv:1705.01933, which was published earlier than this work. This submission has been accepted by Journal "Funkcialaj Ekvacioj"