Vanishing contact structure problem and convergence of the viscosity solutions

doi:10.1080/03605302.2019.1608561

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	Vanishing contact structure problem and convergence of the viscosity solutions
	Chen, Qinbo 1; Cheng, Wei 2; Ishii, Hitoshi 3; Zhao, Kai 2
	2019-09-02
发表期刊	COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS
ISSN	0360-5302
卷号	44 期号:9 页码:801-836
摘要	This article is devoted to studying the vanishing contact structure problem which is a generalization of the vanishing discount problem. Let be a family of Hamiltonians of contact type with parameter and converge to G(x, p). For the contact type Hamilton-Jacobi equation with respect to we prove that, under mild assumptions, the associated viscosity solution converges to a specific viscosity solution u(0) of the vanished contact equation. As applications, we give some convergence results for the nonlinear vanishing discount problem.
关键词	Hamilton-Jacobi equation convergence vanishing discount vanishing contact structure Weak KAM theory Aubry-Mather theory
DOI	10.1080/03605302.2019.1608561
语种	英语
资助项目	China Postdoctoral Science Foundation[2018M641500] ; National Natural Science Foundation of China[11631006] ; National Natural Science Foundation of China[11871267] ; National Natural Science Foundation of China[11790272] ; National Natural Science Foundation of China[16H03948] ; National Natural Science Foundation of China[26220702] ; National Natural Science Foundation of China[18H00833]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000476841600003
出版者	TAYLOR & FRANCIS INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/35269
专题	中国科学院数学与系统科学研究院
通讯作者	Ishii, Hitoshi
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Morningside Ctr Math, Beijing, Peoples R China 2.Nanjing Univ, Dept Math, Nanjing, Jiangsu, Peoples R China 3.Tsuda Univ, Inst Math & Comp Sci, 2-1-1 Tsuda, Kodaira, Tokyo 1878577, Japan
推荐引用方式 GB/T 7714	Chen, Qinbo,Cheng, Wei,Ishii, Hitoshi,et al. Vanishing contact structure problem and convergence of the viscosity solutions[J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS,2019,44(9):801-836.
APA	Chen, Qinbo,Cheng, Wei,Ishii, Hitoshi,&Zhao, Kai.(2019).Vanishing contact structure problem and convergence of the viscosity solutions.COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS,44(9),801-836.
MLA	Chen, Qinbo,et al."Vanishing contact structure problem and convergence of the viscosity solutions".COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS 44.9(2019):801-836.