数学物理学报 ›› 2019, Vol. 39 ›› Issue (5): 1146-1157.

• 论文 • 上一篇    

半线性波动方程Cauchy问题解的生命跨度估计

蒋红标1, 汪海航2   

  1. 1 丽水学院数学系 浙江丽水 323000;
    2 浙江理工大学理学院 杭州 310018
  • 收稿日期:2018-09-27 修回日期:2018-12-24 发布日期:2019-11-08
  • 通讯作者: 汪海航 E-mail:1196443777@qq.com
  • 作者简介:蒋红标,E-mail:hbj@126.com
  • 基金资助:
    浙江省自然科学基金(LY18A010008)

Lifespan Estimation of Solutions to Cauchy Problem of Semilinear Wave Equation

Jiang Hongbiao1, Wang Haihang2   

  1. 1 Department of Mathematics, Lishui University, Zhejiang Lishui 323000;
    2 School of Science, Zhejiang Sci-Tech University, Hangzhou 310018
  • Received:2018-09-27 Revised:2018-12-24 Published:2019-11-08
  • Supported by:
    Supported by the Natural Science Foundation of Zhejiang Province(LY18A010008)

摘要: 该文研究了Rn中半线性波动方程utt-△u=(1+|x|2α|u|p的小初值Cauchy问题解的生命跨度估计.主要利用了改进的Kato型引理,得到了当n=2,1 < p ≤ 2时及n=1,p > 1时改进的生命跨度上界估计.

关键词: 半线性波动方程, 初值问题, 常微分不等式, 生命跨度

Abstract: In this paper, the lifespan estimate to the Cauchy problem of the semi-linear wave equation utt utt-△u=(1+|x|2)α|u|p in Rn is studied. The upper bound of lifespan is improved for the cases n=2,1 < p ≤ 2 and n=1,p > 1, by using the improved Kato's type lemma.

Key words: Semilinear wave equations, Initial value problems, Ordinary differential inequality, Lifespan

中图分类号: 

  • O175