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

doi:10.13371/j.cnki.chin.q.j.m.2021.03.002

Chinese Quarterly Journal of Mathematics ›› 2021, Vol. 36 ›› Issue (3): 235-243.doi: 10.13371/j.cnki.chin.q.j.m.2021.03.002

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

1. College of Data Science, Guangzhou Huashang College, Guangzhou 511300, China; 2. Guangdong AIB Polytechnic College, Guangzhou 510507, China

Received:2021-04-30 Online:2021-09-30 Published:2021-10-08
About author: 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.
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).

Abstract

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

CLC Number:

O175.29

OUYANG Bai-ping, XIAO Sheng-zhong . Blow-Up Result for a Semi-Linear Wave Equation with a Nonlinear Memory Term of Derivative Type[J]. Chinese Quarterly Journal of Mathematics, 2021, 36(3): 235-243.

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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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