ABOUT A CONDITION FOR BLOW UP OF SOLUTIONS OF CAUCHY PROBLEM FOR A WAVE EQUATION

Applied Mathematics and Mechanics (English Edition) ›› 1999, Vol. 20 ›› Issue (9): 1010-1013.

ABOUT A CONDITION FOR BLOW UP OF SOLUTIONS OF CAUCHY PROBLEM FOR A WAVE EQUATION

曹镇潮¹, 王碧祥²

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

收稿日期:1998-02-24 修回日期:1999-05-16 出版日期:1999-09-18 发布日期:1999-09-18
基金资助:
the National Natural Science Foundation of China(19771069)

ABOUT A CONDITION FOR BLOW UP OF SOLUTIONS OF CAUCHY PROBLEM FOR A WAVE EQUATION

Cao Zhenchao¹, Wang Bixiang²

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

Received:1998-02-24 Revised:1999-05-16 Online:1999-09-18 Published:1999-09-18
Supported by:
the National Natural Science Foundation of China(19771069)

摘要/Abstract

摘要： 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<p≤N+1/N-1. In the present work his result allowing 1<p≤N+3/N-1 is improved by using different estimates.

关键词: condition for blow up, wave equation, Cauchy problem

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<p≤N+1/N-1. In the present work his result allowing 1<p≤N+3/N-1 is improved by using different estimates.

Key words: condition for blow up, wave equation, Cauchy problem

中图分类号:

O175.27

曹镇潮;王碧祥. ABOUT A CONDITION FOR BLOW UP OF SOLUTIONS OF CAUCHY PROBLEM FOR A WAVE EQUATION[J]. Applied Mathematics and Mechanics (English Edition), 1999, 20(9): 1010-1013.

Cao Zhenchao;Wang Bixiang. ABOUT A CONDITION FOR BLOW UP OF SOLUTIONS OF CAUCHY PROBLEM FOR A WAVE EQUATION[J]. Applied Mathematics and Mechanics (English Edition), 1999, 20(9): 1010-1013.

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ABOUT A CONDITION FOR BLOW UP OF SOLUTIONS OF CAUCHY PROBLEM FOR A WAVE EQUATION

ABOUT A CONDITION FOR BLOW UP OF SOLUTIONS OF CAUCHY PROBLEM FOR A WAVE EQUATION

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