| 刘法贵.Riemann曲面上耗散双曲几何流的整体经典解[J].数学年刊A辑,2009,30(5):717~726 |
| Riemann曲面上耗散双曲几何流的整体经典解 |
| Global Classical Solutions to the Dissipative Hyperbolic Geometric Flow on Riemann Surfaces |
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| DOI： |
| 中文关键词: 耗散 双曲几何流 Cauchy问题 经典解 破裂 |
| 英文关键词:Dissipation, Hyperbolic geometric flow, Cauchy problem, Classical
solution, Blow up |
| 基金项目:河南省基础研究基金，河南省教育厅自然科学基金(No.2008A110011)资助的项目 |
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| 中文摘要: |
| 基于Einstein方程和Hamilton Ricci流为背景,孔德兴和刘克峰最近提出了耗散双曲几何流的概念.考虑耗散双曲几何流Cauchy问题,证明了对于任意给定的初始度量,总存在初始的对称张量,使得经典解整体存在,并且对应的曲率保持一致有界.否则,其经典解会在有限时间内破裂. |
| 英文摘要: |
| The author considers the Cauchy problem for dissipative hyperbolic geometric
flow equations introduced recently by Kong D. X. and Liu K. F. motivated by Einstein
equation and Hamilton Ricci flow. For the dissipation flow and any given initial metric on
R in certain class of metrics, it is proved that one can always choose suitable initial velocity
symmetric tensor such that the classical global exists for t > 0, and the scalar curvature
R(x, t) corresponding to the solution metric gij(x, t) remains uniformly bounded. Otherwise,
the solution will blow up at a finite time. |
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