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

作　　者：汪玉洁 李霞 WANG Yujie;LI Xia(School of Mathematical Sciences,Suzhou University of Science and Technology,Suzhou 215009,Jiangsu,China.)

机构地区：[1]苏州科技大学数学科学学院,江苏苏州215009

出　　处：《数学年刊（A辑）》2023年第1期17-28,共12页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.11971344);江苏省研究生科研创新计划项目(No.KYCX20-2746)的资助。

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.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.

关 键 词：折现Hamilton-Jacobi方程 粘性解 有限 

分 类 号：O193[理学—数学]