一类非线性波动方程组解的爆破和生命跨度

2016-10-13 09:30吕淑佳
高师理科学刊 2016年2期
关键词:柯西方程组跨度

吕淑佳[1]



一类非线性波动方程组解的爆破和生命跨度

吕淑佳[1]

(中北大学 理学院,山西 太原 030051)

对于一类非线性波动方程组,其中:为波动算子;是在具有紧支集的光滑非负函数;,给出了在不同值情况下,解的爆破和生命跨度.

爆破;生命跨度;柯西问题

对于非线性波动方程组在四维空间的柯西问题

本文主要研究非线性波动方程组

在二维空间下的柯西问题.

通过齐次化原理,在二维非齐次波动方程中,柯西问题(4)的解可以表示为

方程(6)可转化为

同理有

化简式(11),得

的解,得到

综上所述,可得

[1] Li T T,Zhou Y.A note on the life-span of classical solutions to nonlinear wave equations in four space dimensions[J].Indiana University Mathematics Journal,1995,44(4):1207-1248

[2] Lindblad H,Sogge C D.Long-time existence for small amplitude semilinear wave equations[J].American Journal of Mathematics,1996,118(5):1047-1135

[3] Zhou Y,Han W.Life-span of solutions to critical semilinear wave equations[J].Communications in Partial Differential Equations, 2014,39(3):439-451

[4] Takamura H,Wakasa K.The sharp upper bound of the lifespan of solutions to critical semilinear wave equations in high dimensions[J].Journal of Differential Equations,2011,251(4):1157-1171

[5] John F.Blow-up of solutions of nonlinear wave equations in three space dimensions[J].Manuscripta Mathematica,1979,28(1-3): 235-268

[6] John F.Blow-up for quasilinear wave equations in three space dimensions[J].Communications on Pure and Applied Mathematics, 1981,34(1):29-51

[7] Fritz John.Nonlinear wave equations,formation of singularities[M].New York:American Mathematical Soc,1990

[8] John F,Klainerman S.Almost global existence to nonlinear wave equations in three space dimensions[J].Communications on pure and applied mathematics,1984,37(4):443-455

[9] Zhou Y,Han W.Sharpness on the lower bound of the lifespan of solutions to nonlinear wave equations[J].Chinese Annals of Mathematics,Series B,2011,32(4):521-526


Blow up and the lifespan of solutions to some nonlinear wave equations

Lü Shu-jia

(School of Science,North University of China,Taiyuan 030051,China)

For a kind of nonlinear wave equations,whereis the wave operator,is a smooth non-negative function onwith compact support,andis a small parameter,gave that blow up and the lifespan of solutions with different.

blow up;lifespan;Cauchy problem

1007-9831(2016)02-0019-03

O175.27

A

10.3969/j.issn.1007-9831.2016.02.006

2015-10-10

吕淑佳(1989-),女,山西吕梁人,在读硕士研究生,从事双曲型方程组解的适定性研究.E-mail:xiaodoudou422@126.com

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