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Convergence of Viscosity Solutions of Generalized Contact Hamilton-Jacobi Equations
Wang, Ya-Nan1; Yan, Jun2,3; Zhang, Jianlu4,5
2021-05-24
Source PublicationARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
ISSN0003-9527
Pages18
AbstractFor any compact connected manifold M, we consider the generalized contact Hamiltonian H(x, p, u) defined on T*MxR which is convex in p and monotonically increasing in u. Let u(epsilon)(-) : M -> R be the viscosity solution of the parametrized contact Hamilton-Jacobi equation H(x,d(x)u(epsilon)(-)(x),epsilon u(epsilon)(-)(x)) = c(H), with c(H) being the Mane Critical Value. We prove that u(epsilon)(-) converges uniformly, as epsilon -> 0(+), to a specific viscosity solution u(0)(-)0 of the critical equation H(x, d(x)u(0)(-) (x), 0) = c(H), which can be characterized as a minimal combination of the associated Peierls barrier functions.
DOI10.1007/s00205-021-01667-y
Indexed BySCI
Language英语
Funding ProjectNational Natural Science Foundation of China[11901560] ; China Postdoctoral Science Foundation[2017M611439] ; Shanghai Science and Technology Commission[17XD1400500]
WOS Research AreaMathematics ; Mechanics
WOS SubjectMathematics, Applied ; Mechanics
WOS IDWOS:000653602700001
PublisherSPRINGER
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/58639
Collection中国科学院数学与系统科学研究院
Corresponding AuthorWang, Ya-Nan
Affiliation1.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
Recommended Citation
GB/T 7714
Wang, Ya-Nan,Yan, Jun,Zhang, Jianlu. Convergence of Viscosity Solutions of Generalized Contact Hamilton-Jacobi Equations[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS,2021:18.
APA Wang, Ya-Nan,Yan, Jun,&Zhang, Jianlu.(2021).Convergence of Viscosity Solutions of Generalized Contact Hamilton-Jacobi Equations.ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS,18.
MLA Wang, Ya-Nan,et al."Convergence of Viscosity Solutions of Generalized Contact Hamilton-Jacobi Equations".ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS (2021):18.
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