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

作     者：Dexing KONG Qi LIU 孔德兴;刘琦

作者机构：School of Mathematical SciencesZhejiang Universit Department of Applied MathematicsCollege of ScienceZhongyuan University of Technolog 

出 版 物：《Acta Mathematica Scientia》 (数学物理学报（B辑英文版）)

年 卷 期：2018年第38卷第3期

页      面：745-755页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported in part by the NNSF of China(11271323,91330105) the Zhejiang Provincial Natural Science Foundation of China(LZ13A010002) the Science Foundation in Higher Education of Henan(18A110036) 

主　　题：Hyperbolic geometry flow time-dependent damping classical solution energy method global existence 

摘      要：In this article, we investigate the hyperbolic geometry flow with time-dependent dissipation（δ2 gij）/δt2＋μ/（（1 ＋ t）λ）（δ gij）/δt=-2 Rij,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 gij remains uniformly bounded.