Articles

LIFE-SPAN OF CLASSICAL SOLUTIONS TO HYPERBOLIC GEOMETRY FLOW EQUATION IN SEVERAL SPACE DIMENSIONS

  • Dexing KONG ,
  • Qi LIU ,
  • Changming SONG
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  • 1. School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China;
    2. College of Science, Zhongyuan University of Technology, Zhengzhou 450007, China

Received date: 2015-11-04

  Online published: 2017-06-25

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 Henan Provincial Natural Science Foundation of China (152300410226).

Abstract

In this article, we investigate the lower bound of life-span of classical solutions of the hyperbolic geometry flow equations in several space dimensions with "small" initial data. We first present some estimates on solutions of linear wave equations in several space variables. Then, we derive a lower bound of the life-span of the classical solutions to the equations with "small" initial data.

Cite this article

Dexing KONG , Qi LIU , Changming SONG . LIFE-SPAN OF CLASSICAL SOLUTIONS TO HYPERBOLIC GEOMETRY FLOW EQUATION IN SEVERAL SPACE DIMENSIONS[J]. Acta mathematica scientia, Series B, 2017 , 37(3) : 679 -694 . DOI: 10.1016/S0252-9602(17)30030-9

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