非线性记忆项的Euler-Poisson-Darboux-Tricomi方程解的爆破

数学物理学报 ›› 2023, Vol. 43 ›› Issue (1): 169-180.

非线性记忆项的Euler-Poisson-Darboux-Tricomi方程解的爆破

欧阳柏平()

广州华商学院应用数学系广州 511300

收稿日期:2021-10-26 修回日期:2022-08-25 出版日期:2023-02-26 发布日期:2023-03-07
作者简介:欧阳柏平, E-mail: oytengfei79@tom.com
基金资助:
广东省普通高校自然科学重点项目(2019KZDXM042);广东省普通高校创新团队项目(2020WCXTD008);广州华商学院校内项目(2020HSDS01);广州华商学院校内项目(2021HSKT01)

Blow-up of Solutions to the Euler-Poisson-Darboux-Tricomi Equation with a Nonlinear Memory Term

Ouyang Baiping()

Department of Apllied Mathematics, Guangzhou Huashang College, Guangzhou 511300

Received:2021-10-26 Revised:2022-08-25 Online:2023-02-26 Published:2023-03-07
Supported by:
Key Projects of Universities in Guangdong Province (NATURAL SCIENCE)(2019KZDXM042);Innovation Team Project in Colleges and Universities of Guangdong Province(2020WCXTD008);Science Foundation of Guangzhou Huashang College(2020HSDS01);Science Foundation of Guangzhou Huashang College(2021HSKT01)

摘要/Abstract

摘要：

研究了具有非线性记忆项的Euler-Poisson-Darboux-Tricomi方程在次临界情况下解的爆破现象. 利用泛函分析方法结合修正的Bessel方程推出了其柯西问题解的迭代框架和第一下界, 然后通过迭代技巧, 获得了其解的全局非存在性以及解的生命跨度上界估计.

关键词: 非线性记忆项, Euler-Poisson-Darboux-Tricomi方程, 爆破

Abstract:

Blow-up phenomenon of solutions to the Euler-Poisson-Darboux-Tricomi equation with a nonlinear memory term in the subcritical case is studied. By using functional methods associated with a modified Bessel equation, an iteration frame and the first lower bound are derived. Then, nonexistence of global solutions to the Cauchy problem for the Euler-Poisson-Darboux-Tricomi equation and an upper bound estimate of solutions for the lifespan are obtained via the iteration technique.

Key words: Nonlinear memory term, Euler-Poisson-Darboux-Tricomi equation, Blow-up

中图分类号:

O175.2

欧阳柏平. 非线性记忆项的Euler-Poisson-Darboux-Tricomi方程解的爆破[J]. 数学物理学报, 2023, 43(1): 169-180.

Ouyang Baiping. Blow-up of Solutions to the Euler-Poisson-Darboux-Tricomi Equation with a Nonlinear Memory Term[J]. Acta mathematica scientia,Series A, 2023, 43(1): 169-180.

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