| 非紧空间上折现Hamilton-Jacobi方程粘性解的存在性讨论* |
| |
| 引用本文： | 汪玉洁,李 霞.非紧空间上折现Hamilton-Jacobi方程粘性解的存在性讨论*[J].数学年刊A辑(中文版),2023,44(1):17-28. |
| |
| 作者姓名： | 汪玉洁 李 霞 |
| |
| 作者单位： | 苏州科技大学数学科学学院, 江苏, 苏州 215009. |
| |
| 基金项目： | 国家自然科学基金(No.11971344)和江苏省研究生科研创新计划项目(No.KYCX20-2746) |
| |
| 摘 要： | 当底空间紧时, 初始函数为连续函数的Lax-Oleinik型粘性解是局部半凹的,所以是相应的Hamilton-Jacobi\ (以下简称为H-J) 演化方程(简称为接触H-J方程)的粘性解.当底空间非紧时, 对于H-J方程和接触H-J方程, 其Lax-Oleinik型解的下确界未必能取到.文章将探讨在非紧空间上, 折现H-J方程粘性解有限性的条件, 并给出了在此假设下粘性解的表达式.
|
| 关 键 词： | 折现Hamilton-Jacobi方程 粘性解 有限 |
| 收稿时间： | 2021/11/15 0:00:00 |
| 修稿时间： | 2022/12/7 0:00:00 |
The Discussion on the Existence of the Viscosity Solution of the Discounted Hamilton-Jacobi Equation in Non-compact Space |
| |
| WANG Yujie,LI Xia.The Discussion on the Existence of the Viscosity Solution of the Discounted Hamilton-Jacobi Equation in Non-compact Space[J].Chinese Annals of Mathematics,2023,44(1):17-28. |
| |
| Authors: | WANG Yujie LI Xia |
| |
| Institution: | School of Mathematical Sciences, Suzhou University of Science and Technology,Suzhou 215009, Jiangsu, China. |
| |
| Abstract: | If the base space is compact, the viscosity solution with a continuous initial function is locally semi-concave, so it is the viscosity solution of the corresponding Hamilton-Jacobi (H-J for short) evolutionary equation (contact H-J equation for short). If the base space is non-compact, the infimum of the Lax-Oleinik solution of the H-J equation or the contact H-J equation may not be obtained. In this paper, the authors discuss the condition of the viscosity solution of the discounted H-J equation being finite in non-compact space,and give the expression of the viscosity solution under this assumption. |
| |
| Keywords: | Discounted Hamilton-Jacobi equation Viscosity solution Finite |
|
| 点击此处可从《数学年刊A辑(中文版)》浏览原始摘要信息 |
| 点击此处可从《数学年刊A辑(中文版)》下载免费的PDF全文 |
