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

doi:10.1016/S0252-9602(17)30030-9

数学物理学报(英文版) ›› 2017, Vol. 37 ›› Issue (3): 679-694.doi: 10.1016/S0252-9602(17)30030-9

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

孔德兴^1,2, 刘琦¹, 宋长明²

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

收稿日期:2015-11-04 出版日期:2017-06-25 发布日期:2017-06-25
通讯作者: Qi LIU E-mail:21106052@zju.edu.cn
作者简介:Dexing KONG,E-mail:dkong@zju.edu.cn;Changming SONG,E-mail:cmsongh@163.com
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 Henan Provincial Natural Science Foundation of China (152300410226).

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

Dexing KONG^1,2, Qi LIU¹, Changming SONG²

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

Received:2015-11-04 Online:2017-06-25 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).

摘要/Abstract

摘要：

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.

关键词: Hyperbolic geometry flow, classical solution, life-span

Abstract:

Key words: Hyperbolic geometry flow, classical solution, life-span

孔德兴, 刘琦, 宋长明. LIFE-SPAN OF CLASSICAL SOLUTIONS TO HYPERBOLIC GEOMETRY FLOW EQUATION IN SEVERAL SPACE DIMENSIONS[J]. 数学物理学报(英文版), 2017, 37(3): 679-694.

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.

参考文献

[1] Asakura F. Existence of a global solution to a semi-linear wave equation with slowly decreasing initial data in three space dimensions. Comm Part Diff Eq, 1986, 11(13):1459-1487
[2] Hörmannder L. Lectures on Nonlinear Hyperbolic Differential Equations. Mathématatique and Applications, 1997
[3] Hörmannder L. L¹, L^∞ estimates for the wave operator//Bordas L. Analyse mathematique et applications. Paris:Gauthier-Villars, 1988:211-234
[4] Klainerman S. Global existence for nonlinear wave equation. Comm Pure Appl Math, 1980, 33(1):43-101
[5] Klainerman S. Uniform decay estimates and the lorentz invariance of the classical wave equations. Comm Pure Appl Math, 1985, 38(3):321-332
[6] Klainerman S. Remaks on the global Sobolev inequalities in the Minkowski space Rⁿ⁺¹. Comm Pure Appl Math, 1987, 40(1):111-116
[7] Kong D X. Life-span of classical solutions to quasilinear reducible hyperbolic system and its applications. Chin Ann Math, 1992, 13(2):188-195
[8] Kong D X. Hyperbolic geometry flow//The proceedings of ICCM 2007. Vol Ⅱ. Beijing:Higher Educational Press, 2007:95-110
[9] Kong D X, Liu K F. Wave character of metric and hyperbolic geometry flow. J Math Phys, 2007, 48(10):103508
[10] Kong D X, Liu K F, Wang Y Z. Life-span of classical solutions to hyperbolic geometry flow in two space variables with decay initial data. Comm Part Diff Eq, 2010, 36(1):162-184
[11] Kong D X, Liu K F, Xu D L. The hyperbolic geometry flow on Riemann surfaces. Comm Part Diff Eq, 2009, 34(4/5):553-580
[12] Li T T, Zhou Y. Lifespan of classical solutions to fully nonlinear wave equations Ⅱ. Nonlinear Analysis, Theory, Methods and Applications, 1992, 19(9):833-453
[13] Lindblad H. On the lifespan of solutions of nonlinear wave equations with small initial data. Comm Pure Appl Math, 1990, 43(4):445-472
[14] Liu F G, Zhang Z Y. Global classical solutions to hyperbolic geometric flow on Riemann surfaces. Pacific J Math, 2010, 246(2):333-343
[15] Sogge C D. Lectures on Nonlinear Wave Equation. Monographs in analysis. Ⅱ. Someerville, MA:International Press, 1994

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

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

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