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

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

Acta mathematica scientia,Series B ›› 2017, Vol. 37 ›› Issue (3): 679-694.doi: 10.1016/S0252-9602(17)30030-9

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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).

Abstract

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.

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[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

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