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

被引：0
|
作者：
孔德兴 [1 ]
刘琦 [2 ]
机构：
[1] School of Mathematical Sciences, Zhejiang University
[2] Department of Applied Mathematics, College of Science, Zhongyuan University of Technology
来源：
Acta Mathematica Scientia | 2018年 / 03期
关键词：
Hyperbolic geometry flow; time-dependent damping; classical solution; energy method; global existence;
D O I：
暂无
中图分类号：
O175 [微分方程、积分方程];
学科分类号：
070104 ;
摘要：
In this article, we investigate the hyperbolic geometry flow with time-dependent dissipation(?;g;)/? t;+μ/(（1 + t）;)(? g;)/? t=-2 R;,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 gij 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;remains uniformly bounded.
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页码：745 / 755
页数：11
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