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A Numerical Study of Blowup in the harmonic map Heat Flow Using the MMPDE Moving Mesh Method

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Numerical Mathematics(Theory,Methods and Applications) 2013年第2期6卷 364-383页

作者： Ronald D.Haynes Weizhang Huang Paul A.Zegeling Department of Mathematics and Statistics Memorial University of NewfoundlandSt.John’sNL A1C 5S7Canada Department of Mathematics University of KansasLawrenceKS 66045USA Department of Mathematics Utrecht UniversityUtrechtThe Netherlands

The numerical solution of the harmonic heat map flow problems with blowup in finite or infinite time is considered using an adaptive moving mesh method.A properly chosen monitor function is derived so that the moving mesh method can be used to simulate blowup and produce accurate blowup profiles which agree with formal asymptotic ***,the moving mesh method has finite time blowup when the underlying continuous problem *** situations where the continuous problem has infinite time blowup,the moving mesh method exhibits finite time blowup with a blowup time tending to infinity as the number of mesh points *** inadequacy of a uniform mesh solution is clearly demonstrated.

关键词： Heat flow harmonic map blowup moving mesh method finite difference

harmonic maps from Kahler Manifolds

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Acta Mathematica Sinica,English Series 1999年第2期15卷 277-292页

作者： Yuanlong Xin, Institute of Mathematics and LMNS, Fudan University, Shanghai 200433, P. R. ChinaE-mail: ylxin@fudan, edu. cn Institute of Mathematics and LMNS Fudan University Shanghai P. R. China

Some Liouville type theorems for harmonic maps from Kahler manifolds are obtained. The main result is to prove that a harmonic map from a bounded symmetric domain (except IV（2）) to any Riemannian manifold with finit... 详细信息

关键词： harmonic map Kahler manifold Bounded symmetric domain

harmonic mapS AND FUNDAMENTAL GROUPS OF NONPOSITIVELY CURVEDRIEMANNIAN MANIFOLDS

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Chinese Annals of Mathematics,Series B 1996年第4期17卷 491-496页

作者：沈纯理周青 E CHINA NORMAL UNIV DEPT MATHSHANGHAI 200062PEOPLES R CHINA

Using the theory of harmonic maps the authors discuss theproperties of the fundamental group of a complete nonpositivelycurved Riemannian manifold, and prove that the finitely generatedvirtual solvable subgroup of fundamental group of a completenonpositively curved Riemannian manifold either is a peripheralsubgroup of fundamental group or can be realized by animmersed totall geodesic closed flat manifold. It generalizessome results of Gromoll-Wolf, Lawson-Yan and Schoen-Yau.

关键词： harmonic map Riemannian manifold Fundamental group

THE HEAT FLOW OF harmonic mapS FROM NONCOMPACT MANIFOLDS

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Chinese Annals of Mathematics,Series B 2000年第1期21卷 121-130页

作者： WANGSILEI LIJIAYU InstituteofMathematics AcademiaSinicaBeijing100080China. DepartmentofMathematics HangzhouUniversityHangzhou310028China.

The authors consider the global existence of the heat flow of harmonic maps from noncompact manifolds while imposing restrictions on the initial data.

关键词： Heat flow Noncompact manifold harmonic map

On the Regularity Theories for harmonic maps from Finsler Manifolds

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Chinese Annals of Mathematics,Series B 2012年第4期33卷 595-600页

作者： Wei ZHU Department of Mathematics Zhejiang University Hangzhou 310027 China.

The author studies the regularity of energy minimizing maps from Finsler manifolds to Riemannian manifolds. It is also shown that the energy minimizing maps are smooth, when the target manifolds have no focal points.

关键词： Finsler manifolds harmonic map Regularity

Heat flow of harmonic maps from noncompact manifolds

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Applied Mathematics(A Journal of Chinese Universities) 2008年第4期23卷 431-436页

作者： WANG Meng LIU Xiao-feng Dept. of Math. Zhejiang Univ. Hangzhou 310027 China Dept. of Appl. Math. Donghua Univ. Shanghai 201620 China

The global existence of the heat flow for harmonic maps from noncompact manifolds is considered. When L^m norm of the gradient of initial data is small, the existence of a global solution is proved.

关键词： heat flow noncompact complete manifold harmonic map

Factorization and symplectic uniton numbers for harmonic maps into symplectic groups

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Science China Mathematics 2001年第10期44卷 1225-1235页

作者：贺群沈一兵 1. Department of Mathematics West-Brook Campus Zhejiang University 310028 Hangzhou China 2. Department of Applied Mathematics Shanghai Tongji University 200092 Shanghai China

It is proved that any harmonic map (?): Ω→Sp(N) from a simply connected domain Ω (?) R2∪ {∞} into the symplectic group Sp(N)(?)U(2N) with finite uniton number can be factorized into a product of a finite number of symplectic unitons. Based on this factorization, it is proved that the mini-mal symplectic uniton number of (?) is not larger than N, and the minimal uniton number of (?) is not larger than 2N - 1. The latter has been shown in literature in a quite different way.

关键词： harmonic map symplectic group factorization uniton number.

ON harmonic mapS INTO SYMPLECTIC GROUPS Sp(N)

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Chinese Annals of Mathematics,Series B 2001年第4期22卷 519-528页

作者： HEQUN SHENYIBING DepartmentofAppliedMathematics TongjiUniversityShanghai200092China. DepartmentofMathematics West-BrookZhejiangUniversityHangzhou310028China.

By means of the theory of harmonic maps into the unitary group U(N), the authors study harmonic maps into the symplectic group Sp(N). The symplectic uniton and symplectic ex--tended uniton are introduced. The method of the symplectic Backlund transformation and the Darboux transformation is used to construct new symplectic unitons from a known one.

关键词： harmonic map Symplectic group Symplectic uniton Darboux transformation

Existence for V T-harmonic maps from compact manifolds with boundary

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Science China Mathematics 2022年第11期65卷 2371-2378页

作者： Xiangzhi Cao Qun Chen School of Information Engineering Nanjing Xiaozhuang UniversityNanjing 211171China School of Mathematics and Statistics Wuhan UniversityWuhan 430072China

We consider a kind of generalized harmonic maps,namely,the V T-harmonic *** prove an existence theorem for the Dirichlet problem of V T-harmonic maps from compact manifolds with boundary.

关键词： Dirichlet problem existence harmonic map