数学季刊 >

2021 , Vol. 36 >Issue 3: 235 - 243

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2021.03.002

一类具有导数型非线性记忆项的半线性波动方程的爆破结果

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  • 1. College of Data Science, Guangzhou Huashang College, Guangzhou 511300, China; 2. Guangdong AIB Polytechnic College, Guangzhou 510507, China
OUYANG Bai-ping (1979-), male, native of Chenzhou, Hunan, lecturer of Guangzhou Huashang College, engages in PDEs; XIAO Sheng-zhong (1965-), male, native of Shaoyang, Hunan, professor of Guangdong AIB Polytechnic College, engages in PDEs.

收稿日期: 2021-04-30

  网络出版日期: 2021-07-15

基金资助

 Supported by the Natural Science Foundation of China (Grant No. 11371175); Innovation Team Project in Colleges and Universities of Guangdong Province (Grant No. 2020WCXTD008); Science Foundation of Huashang College Guangdong University of Finance & Economics (Grant No. 2020HSDS01); Science Research Team Project in Guangzhou Huashang College (Grant No. 2021HSKT01).

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Blow-Up Result for a Semi-Linear Wave Equation with a Nonlinear Memory Term of Derivative Type

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  • 1. College of Data Science, Guangzhou Huashang College, Guangzhou 511300, China; 2. Guangdong AIB Polytechnic College, Guangzhou 510507, China
OUYANG Bai-ping (1979-), male, native of Chenzhou, Hunan, lecturer of Guangzhou Huashang College, engages in PDEs; XIAO Sheng-zhong (1965-), male, native of Shaoyang, Hunan, professor of Guangdong AIB Polytechnic College, engages in PDEs.

Received date: 2021-04-30

  Online published: 2021-07-15

Supported by

 Supported by the Natural Science Foundation of China (Grant No. 11371175); Innovation Team Project in Colleges and Universities of Guangdong Province (Grant No. 2020WCXTD008); Science Foundation of Huashang College Guangdong University of Finance & Economics (Grant No. 2020HSDS01); Science Research Team Project in Guangzhou Huashang College (Grant No. 2021HSKT01).

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摘要

 In this paper, we study the blow-up of solutions to a semi-linear wave equation with a nonlinear memory term of derivative type. By using methods of an iteration argument and differential inequalities, we obtain the blow-up result for the semi-linear wave equation when the exponent of p is under certain conditions. Meanwhile, we derive an upper bound of the lifespan of solutions to the Cauchy problem for the semi-linear wave equation.

关键词： Semi-linear wave equation; Blow-up; Nonlinear memory term of derivative type; Lifespan

本文引用格式

欧阳柏平, 肖胜中 . 一类具有导数型非线性记忆项的半线性波动方程的爆破结果[J]. 数学季刊, 2021 , 36(3) : 235 -243 . DOI: 10.13371/j.cnki.chin.q.j.m.2021.03.002

Abstract

In this paper, we study the blow-up of solutions to a semi-linear wave equation with a nonlinear memory term of derivative type. By using methods of an iteration argument and differential inequalities, we obtain the blow-up result for the semi-linear wave equation when the exponent of p is under certain conditions. Meanwhile, we derive an upper bound of the lifespan of solutions to the Cauchy problem for the semi-linear wave equation.

Key words： Semi-linear wave equation; Blow-up; Nonlinear memory term of derivative type; Lifespan

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