非紧Riemann流形上一类Kazdan-Warner 型方程光滑解的存在唯一性

邓义华

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非紧Riemann流形上一类Kazdan-Warner 型方程光滑解的存在唯一性

研究论文 | 更新时间：2023-12-11

- 非紧Riemann流形上一类Kazdan-Warner 型方程光滑解的存在唯一性
- Existence and Uniqueness of Smooth Solution to a Class of Kazdan-Warner Typed Equations on NonCompact Riemannian Manifolds
- 角色： First author , 第一作者 ,
  
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  衡阳师范学院数学与计算科学系,湖南,衡阳,421008
  
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  邓义华
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- 中山大学学报(自然科学版)(中英文) 2010年49卷第6期页码：26-30
- 作者机构：
  
  衡阳师范学院数学与计算科学系,湖南,衡阳,421008
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- 纸质出版日期：2010，
  
  网络出版日期：2010-11-25，
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邓义华. 非紧Riemann流形上一类Kazdan-Warner 型方程光滑解的存在唯一性[J]. 中山大学学报(自然科学版)(中英文), 2010,49(6):26-30.

DENG Yihua. Existence and Uniqueness of Smooth Solution to a Class of Kazdan-Warner Typed Equations on NonCompact Riemannian Manifolds[J]. Acta Scientiarum Naturalium Universitatis SunYatseni, 2010,49(6):26-30.
邓义华. 非紧Riemann流形上一类Kazdan-Warner 型方程光滑解的存在唯一性[J]. 中山大学学报(自然科学版)(中英文), 2010,49(6):26-30. DOI：

DENG Yihua. Existence and Uniqueness of Smooth Solution to a Class of Kazdan-Warner Typed Equations on NonCompact Riemannian Manifolds[J]. Acta Scientiarum Naturalium Universitatis SunYatseni, 2010,49(6):26-30. DOI：

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摘要

在非紧Riemann流形上讨论了一类Kazdan-Warner 型方程。首先，利用穷竭法以及标准的抛物理论得到了一类带初始条件和Neumann边界条件的热流方程长时间解的存在唯一性。然后得到了热流方程解的一致估计并在合适的条件下得到了所讨论方程光滑解的存在唯一性。

译

Abstract

A class of KazdanWarner typed equations on noncompact Riemannian manifolds are discussed. Firstly, the existence and uniqueness of longtime solution to the corresponding heat equation with initial condition and Neumann boundary condition are obtained by the exhaustion method and the standard parabolic theory. And then, some uniform estimates of the solution to the heat equation are obtained and the existence and uniqueness of smooth solution to the equations discussed in this paper are gained under suitable conditions.

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关键词

非紧Riemann流形; Kazdan-Warner型方程; 热流方程; 穷竭法

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Keywords

noncompact Riemannian manifolds; KazdanWarner typed equation; heat equation; exhaustion method

译

摘要

Abstract

A class of KazdanWarner typed equations on noncompact Riemannian manifolds are discussed. Firstly

the existence and uniqueness of longtime solution to the corresponding heat equation with initial condition and Neumann boundary condition are obtained by the exhaustion method and the standard parabolic theory. And then

some uniform estimates of the solution to the heat equation are obtained and the existence and uniqueness of smooth solution to the equations discussed in this paper are gained under suitable conditions.

关键词

非紧Riemann流形Kazdan-Warner型方程热流方程穷竭法

Keywords

noncompact Riemannian manifoldsKazdanWarner typed equationheat equationexhaustion method

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