GLOBAL EXISTENCE OF CLASSICAL SOLUTIONS TO THE HYPERBOLIC GEOMETRY FLOW WITH TIME-DEPENDENT DISSIPATION

doi:10.1016/S0252-9602(18)30780-X

数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (3): 745-755.doi: 10.1016/S0252-9602(18)30780-X

• 论文 • 下一篇

GLOBAL EXISTENCE OF CLASSICAL SOLUTIONS TO THE HYPERBOLIC GEOMETRY FLOW WITH TIME-DEPENDENT DISSIPATION

孔德兴¹, 刘琦²

1. School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China;
2. Department of Applied Mathematics, College of Science, Zhongyuan University of Technology, Zhengzhou 450007, China

收稿日期:2016-12-12 修回日期:2017-09-20 出版日期:2018-06-25 发布日期:2018-06-25
通讯作者: Qi LIU E-mail:21106052@zju.edu.cn
作者简介:Dexing KONG,E-mail:dkong@zju.edu.cn
基金资助:
This work is supported in part by the NNSF of China (11271323, 91330105), the Zhejiang Provincial Natural Science Foundation of China (LZ13A010002), and the Science Foundation in Higher Education of Henan (18A110036).

GLOBAL EXISTENCE OF CLASSICAL SOLUTIONS TO THE HYPERBOLIC GEOMETRY FLOW WITH TIME-DEPENDENT DISSIPATION

Dexing KONG¹, Qi LIU²

1. School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China;
2. Department of Applied Mathematics, College of Science, Zhongyuan University of Technology, Zhengzhou 450007, China

Received:2016-12-12 Revised:2017-09-20 Online:2018-06-25 Published:2018-06-25
Contact: Qi LIU E-mail:21106052@zju.edu.cn
Supported by:
This work is supported in part by the NNSF of China (11271323, 91330105), the Zhejiang Provincial Natural Science Foundation of China (LZ13A010002), and the Science Foundation in Higher Education of Henan (18A110036).

摘要/Abstract

摘要：

In this article, we investigate the hyperbolic geometry flow with time-dependent dissipation
(∂²g_ij)/(∂t²) + μ/((1 + t)^λ) (∂g_ij)/∂t=-2R_ij,
on Riemann surface. On the basis of the energy method, for 0 < λ ≤ 1, μ > λ + 1, we show that there exists a global solution g_ij to the hyperbolic geometry flow with time-dependent dissipation with asymptotic flat initial Riemann surfaces. Moreover, we prove that the scalar curvature R(t, x) of the solution metric g_ij remains uniformly bounded.

关键词: Hyperbolic geometry flow, time-dependent damping, classical solution, energy method, global existence

Abstract:

Key words: Hyperbolic geometry flow, time-dependent damping, classical solution, energy method, global existence

孔德兴, 刘琦. GLOBAL EXISTENCE OF CLASSICAL SOLUTIONS TO THE HYPERBOLIC GEOMETRY FLOW WITH TIME-DEPENDENT DISSIPATION[J]. 数学物理学报(英文版), 2018, 38(3): 745-755.

Dexing KONG, Qi LIU. GLOBAL EXISTENCE OF CLASSICAL SOLUTIONS TO THE HYPERBOLIC GEOMETRY FLOW WITH TIME-DEPENDENT DISSIPATION[J]. Acta mathematica scientia,Series B, 2018, 38(3): 745-755.

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GLOBAL EXISTENCE OF CLASSICAL SOLUTIONS TO THE HYPERBOLIC GEOMETRY FLOW WITH TIME-DEPENDENT DISSIPATION

GLOBAL EXISTENCE OF CLASSICAL SOLUTIONS TO THE HYPERBOLIC GEOMETRY FLOW WITH TIME-DEPENDENT DISSIPATION

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