| 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,2023,44(1):17~28 |
| 非紧空间上折现Hamilton-Jacobi方程粘性解的存在性讨论* |
| The Discussion on the Existence of the Viscosity Solution of the Discounted Hamilton-Jacobi Equation in Non-compact Space |
| Received:November 15, 2021 Revised:December 07, 2022 |
| DOI：10.16205/j.cnki.cama.2023.0002 |
| 中文关键词: 折现Hamilton-Jacobi方程 , 粘性解, 有限 |
| 英文关键词:Discounted Hamilton-Jacobi equation, Viscosity solution, Finite |
| 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) |
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| 中文摘要: |
| 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. |
| 英文摘要: |
| 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. |
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