常微分不等式及其在半线性波动方程的应用

数学物理学报 ›› 2020, Vol. 40 ›› Issue (5): 1319-1332.

常微分不等式及其在半线性波动方程的应用

黄守军*(),孟希望()

^{安徽师范大学数学与统计学院安徽芜湖 241002}

收稿日期:2019-03-29 出版日期:2020-10-26 发布日期:2020-11-04
通讯作者: 黄守军 E-mail:sjhuang@ahnu.edu.cn;3572861950@qq.com
作者简介:孟希望, E-mail:3572861950@qq.com
基金资助:
国家自然科学基金(11301006);安徽省自然科学基金(1408085MA01)

Improved Ordinary Differential Inequality and Its Application to Semilinear Wave Equations

Shoujun Huang*(),Xiwang Meng()

^{School of Mathematics and Statistics, Anhui Normal University, Anhui Wuhu 241002}

Received:2019-03-29 Online:2020-10-26 Published:2020-11-04
Contact: Shoujun Huang E-mail:sjhuang@ahnu.edu.cn;3572861950@qq.com
Supported by:
the NSFC(11301006);the NSF of Anhui Province(1408085MA01)

摘要/Abstract

摘要：

该文首先得到两类变系数的常微分不等式的爆破结果，可视为文献[3，定理3.1]的推广.其次，作为改进的常微分不等式的一个应用，考虑具有尺度不变阻尼项的半线性波动方程的柯西问题，给予初值合理假设，得到当$\mu>1$和$1< p < 1+\frac{2}{n}$时解的生命跨度的上界估计.该结果的证明方法主要来自于文献[11].

关键词: 常微分不等式, 半线性波动方程, 生命跨度

Abstract:

In this paper, we first derive some blow-up results for two ordinary differential inequalities with variable coefficients, which are the generalizations of Theorem 3.1 in Li and Zhou^[3]. Second, as an application of the improved ordinary differential inequality, we consider the Cauchy problem for the semilinear wave equation with scale-invariant damping and deduce the upper bound of the lifespan for the case $\mu>1$ and $ 1 < p < 1+\frac{2}{n}$ under some suitable assumptions for the initial data. The method for the latter result is due to Lai and Zhou^[11].

Key words: Ordinary differential inequality, Semilinear wave equation, Lifespan

中图分类号:

O175.2

黄守军,孟希望. 常微分不等式及其在半线性波动方程的应用[J]. 数学物理学报, 2020, 40(5): 1319-1332.

Shoujun Huang,Xiwang Meng. Improved Ordinary Differential Inequality and Its Application to Semilinear Wave Equations[J]. Acta mathematica scientia,Series A, 2020, 40(5): 1319-1332.

参考文献 19

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