On the Negative Limit of Viscosity Solutions for Discounted Hamilton-Jacobi Equations

doi:10.1007/s10884-022-10227-1

CSpace

	On the Negative Limit of Viscosity Solutions for Discounted Hamilton-Jacobi Equations
	Wang, Ya-Nan 1; Yan, Jun 2,3; Zhang, Jianlu 4,5
	2022-11-24
发表期刊	JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS
ISSN	1040-7294
页码	19
摘要	Suppose M is a closed Riemannian manifold. For a C-2 generic (in the sense of Mane) Tonelli Hamiltonian H : T* M -> R, the minimal viscosity solution u(lambda)(-) : M -> R of the negative discounted equation -lambda u + H(x, d(x)u) = c(H), x is an element of M , lambda > 0 with the Mane's critical value c(H) converges to a uniquely established viscosity solution u(0)(-) of the critical Hamilton-Jacobi equation H (x, d(x)u) = c(H), x is an element of M as lambda -> 0(+). We also propose a dynamical interpretation of u(0)(-).
关键词	Discounted Hamilton-Jacobi equation Viscosity solution Conjugated weak KAM solutions Aubry Mather sets Mane's genericity
DOI	10.1007/s10884-022-10227-1
收录类别	SCI
语种	英语
资助项目	National Key Research and Development Program of China[2022YFA1007500] ; National Natural Science Foundation of China[11501437] ; Shanghai Science and Technology Commission[17XD1400500]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000888685900002
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/60569
专题	中国科学院数学与系统科学研究院
通讯作者	Zhang, Jianlu
作者单位	1.Nanjing Normal Univ, Sch Math Sci, Nanjing 210097, Peoples R China 2.Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China 3.Shanghai Key Lab Contemporary Appl Math, Shanghai 200433, Peoples R China 4.Chinese Acad Sci, Acad Math & Syst Sci, Hua Loo Keng Key Lab Math, Beijing 100190, Peoples R China 5.Chinese Acad Sci, Acad Math & Syst Sci, Math Inst, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Wang, Ya-Nan,Yan, Jun,Zhang, Jianlu. On the Negative Limit of Viscosity Solutions for Discounted Hamilton-Jacobi Equations[J]. JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS,2022:19.
APA	Wang, Ya-Nan,Yan, Jun,&Zhang, Jianlu.(2022).On the Negative Limit of Viscosity Solutions for Discounted Hamilton-Jacobi Equations.JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS,19.
MLA	Wang, Ya-Nan,et al."On the Negative Limit of Viscosity Solutions for Discounted Hamilton-Jacobi Equations".JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS (2022):19.