非紧空间上折现Hamilton-Jacobi方程的粘性解

doi:10.3969/j.issn.1000-5641.2022.02.002

华东师范大学学报（自然科学版） ›› 2022, Vol. 2022 ›› Issue (2): 9-15.doi: 10.3969/j.issn.1000-5641.2022.02.002

非紧空间上折现Hamilton-Jacobi方程的粘性解

陈苏婷, 李霞*()

苏州科技大学数学科学学院, 江苏苏州　215009

收稿日期:2020-10-13 出版日期:2022-03-25 发布日期:2022-03-28
通讯作者: 李霞 E-mail:lixia0527@188.com
基金资助:
国家自然科学基金(11971344)

The viscosity solution of the discounted Hamilton-Jacobi equation in non-compact space

Suting CHEN, Xia LI*()

School of Mathematical Sciences, Suzhou University of Science and Technology, Suzhou Jiangsu　215009, China

Received:2020-10-13 Online:2022-03-25 Published:2022-03-28
Contact: Xia LI E-mail:lixia0527@188.com

摘要/Abstract

摘要：

折现Hamilton-Jacobi方程(简称H-J方程)作为接触H-J方程的一种特殊形式, 对其研究具有深刻意义. 研究了折现H-J方程在底空间非紧时粘性解的一个表达式 $u_{\lambda}(x,t)$ . 就一个具体的折现H-J方程, 探讨了在底空间非紧且 $\lambda>0$ 时, 在不同初值情形下, $u_{\lambda}(x,t)$ 在 $t \rightarrow +\infty $ 时的收敛情况.

关键词: Hamilton-Jacobi方程, 接触系统, 粘性解

Abstract:

The discounted Hamilton-Jacobi equation (H-J equation) is a special form of the contact Hamilton-Jacobi equation; hence, study of the discounted H-J equation is important. In this article, we first study an expression of the viscosity solution $u_{\lambda}(x,t)$ for the discounted H-J equation in non-compact space. Then, we explore the convergence of the viscosity solution $u_{\lambda}(x,t)$ for a specific discounted H-J equation with $\lambda >0$ in non-compact space for the initial value in different cases.

Key words: Hamilton-Jacobi equation, contact system, viscosity solution

中图分类号:

O193

陈苏婷, 李霞. 非紧空间上折现Hamilton-Jacobi方程的粘性解[J]. 华东师范大学学报（自然科学版）, 2022, 2022(2): 9-15.

Suting CHEN, Xia LI. The viscosity solution of the discounted Hamilton-Jacobi equation in non-compact space[J]. Journal of East China Normal University(Natural Science), 2022, 2022(2): 9-15.

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非紧空间上折现Hamilton-Jacobi方程的粘性解

The viscosity solution of the discounted Hamilton-Jacobi equation in non-compact space

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