数学物理学报(英文版) ›› 2003, Vol. 23 ›› Issue (1): 16-22.

• 论文 • 上一篇    下一篇

REMARKS ON THE LIFESPAN FOR THE SOLUTION TO NONLINEAR WAVE EQUATIONS IN THREE SPACE DIMENSIONS

 杨晗, 刘法贵   

  1. Department of Applied Mathematics, South West Jiaotong University, Chengdu 610031, China North China Institute of Water Conservancy and Hydroeletric Power, Zhengzhou 450045, China
  • 出版日期:2003-01-06 发布日期:2003-01-06
  • 基金资助:

    This work was supported by South-West Jiaotong University Foundation

REMARKS ON THE LIFESPAN FOR THE SOLUTION TO NONLINEAR WAVE EQUATIONS IN THREE SPACE DIMENSIONS

 YANG Han, LIU Fa-Gui   

  1. Department of Applied Mathematics, South West Jiaotong University, Chengdu 610031, China North China Institute of Water Conservancy and Hydroeletric Power, Zhengzhou 450045, China
  • Online:2003-01-06 Published:2003-01-06
  • Supported by:

    This work was supported by South-West Jiaotong University Foundation

PDF (PC)

922

摘要：

The authors consider the Cauchy problem for the following nonlinear wave equations
?????
utt − u = |∇v|2,
vtt − v = (u)2,
u(0, x) = "u0(x), ut(0, x) = "u1(x),
v(0, x) = "v0(x), vt(0, x) = "v1(x),
where x ∈ R3, t ≥ 0, " > 0 is a small parameter, and obtain the sharp bounds for the lifespan of solution to (0.1). Specially, it is proved that there exist two constants C1 and C2, which are independent of ", then the lifespan T(") satisfies the folowing inequalities C1 ≤ lim"!0 " ln T(") ≤ C2.

关键词: Nonlinear wave equations, lifespan, spherical mean

Abstract:

The authors consider the Cauchy problem for the following nonlinear wave equations
?????
utt − u = |∇v|2,
vtt − v = (u)2,
u(0, x) = "u0(x), ut(0, x) = "u1(x),
v(0, x) = "v0(x), vt(0, x) = "v1(x),
where x ∈ R3, t ≥ 0, " > 0 is a small parameter, and obtain the sharp bounds for the lifespan of solution to (0.1). Specially, it is proved that there exist two constants C1 and C2, which are independent of ", then the lifespan T(") satisfies the folowing inequalities C1 ≤ lim"!0 " ln T(") ≤ C2.

Key words: Nonlinear wave equations, lifespan, spherical mean

中图分类号: 

  • 35L70
版权所有 © 《数学物理学报(英文版)》杂志社
地址：武汉市71010号信箱(430071)　电话: 027-87199206(中文版)　027-87199087(英文版)
E-mail: actams@apm.ac.cn
本系统由北京玛格泰克科技发展有限公司设计开发