半线性波动方程Cauchy问题解的生命跨度估计

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

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 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 出版日期:2019-10-26 发布日期:2019-11-08
通讯作者: 汪海航 E-mail:hbj@126.com;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

Hongbiao Jiang¹(),Haihang Wang^2,*()

¹ Department of Mathematics, Lishui University, Zhejiang Lishui 323000
² School of Science, Zhejiang Sci-Tech University, Hangzhou 310018

Received:2018-09-27 Online:2019-10-26 Published:2019-11-08
Contact: Haihang Wang E-mail:hbj@126.com;1196443777@qq.com
Supported by:
the Natural Science Foundation of Zhejiang Province(LY18A010008)

摘要/Abstract

摘要：

该文研究了${\mathbb{R}}$ⁿ中半线性波动方程u_tt-△u=（1+|x|²）^α|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 u_tt-△u=(1+|x|²)^α|u|^p in ${\mathbb{R}}$ⁿ 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

蒋红标,汪海航. 半线性波动方程Cauchy问题解的生命跨度估计[J]. 数学物理学报, 2019, 39(5): 1146-1157.

Hongbiao Jiang,Haihang Wang. Lifespan Estimation of Solutions to Cauchy Problem of Semilinear Wave Equation[J]. Acta mathematica scientia,Series A, 2019, 39(5): 1146-1157.

参考文献

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