About a Conditon for Blow up of Solutions of Cauchy Problem for a Wave Equation

Cao Zhenchao; Wang Bixiang

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Cao Zhenchao, Wang Bixiang. About a Conditon for Blow up of Solutions of Cauchy Problem for a Wave Equation[J]. Applied Mathematics and Mechanics, 1999, 20(9): 943-946.

Citation:

Cao Zhenchao, Wang Bixiang. About a Conditon for Blow up of Solutions of Cauchy Problem for a Wave Equation[J]. Applied Mathematics and Mechanics, 1999, 20(9): 943-946.

Citation:

Cao Zhenchao, Wang Bixiang. About a Conditon for Blow up of Solutions of Cauchy Problem for a Wave Equation[J]. Applied Mathematics and Mechanics, 1999, 20(9): 943-946.

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About a Conditon for Blow up of Solutions of Cauchy Problem for a Wave Equation

Cao Zhenchao¹,
Wang Bixiang²

1.
Department of Mathematics, Xiamen University, Xiamen, Fujian 361005, P R China;
2.
Department of Applled Mathematics, Tsinghua University, Beijing 100084, P R China

Received Date: 1998-02-24
Rev Recd Date: 1999-05-16
Publish Date: 1999-09-15

Abstract

Abstract
For the nonlinear wave equation in R^N×R⁺(N≥2):∂²u(x,t)/∂t²-∂/∂x_i[a_ij(x)∂/∂x_ju=|u|^p-1·u,in 1980 Kato proved the solution of Cauchy problem may blow up in finite time if 1
- condition for blow up,
- wave equation,
- Cauchy problem

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References(2)

References

[1]	Kato T.Blow up ofsolutions ofsome nonlinear hyperbolic equations[J].Comm Pure Appl Math,1980,33(4):501~505.
[2]	Cao Zhenchao,Wang Bixiang,Guo Boling.Global existence theory for the two dimen sional derivative G-Lequation[J].Chinese Science Bulletin,1998,43(5):393~395.