伪抛物型 p-Kirchhoff 方程的爆破解

数学物理学报 ›› 2024, Vol. 44 ›› Issue (3): 717-736.

伪抛物型 p-Kirchhoff 方程的爆破解

李锋杰^*(),李平

中国石油大学(华东) 山东青岛 266580

收稿日期:2023-05-19 修回日期:2023-10-14 出版日期:2024-06-26 发布日期:2024-05-17
通讯作者: *李锋杰，E-mail:fjli@upc.edu.cn
基金资助:
山东省自然科学基金面上项目(ZR2021MA003)

Blow-up Solutions in a p-Kirchhoff Equation of Pseudo-Parabolic Type

Li Fengjie^*(),Li Ping

College of Science, China University of Petroleum, Shandong Qingdao 266580

Received:2023-05-19 Revised:2023-10-14 Online:2024-06-26 Published:2024-05-17
Supported by:
Shandong Provincial Natural Science Foundation of China(ZR2021MA003)

摘要/Abstract

摘要：

该文研究了一类具有变指数的伪抛物型 p-Kirchhoff 方程的齐次 Dirichlet 初边值问题. 首先, 采用改进的势阱法和辅助函数法, 对初始能量进行最优分类, 得到解的爆破和整体存在的判据. 其次, 分别得到了解的爆破时间估计和整体解的大时间性态.

关键词: 伪抛物型 p-Kirchhoff 方程, 大时间性态, 爆破时间, 初始能量, 变指数

Abstract:

This paper deals with a homogeneous Dirichlet initial-boundary value problem of the p-Kirchhoff pseudo-parabolic equation involving a variable exponent. Firstly, we give the optimal classification of initial energy by using modified potential well method and the auxiliary function method and obtain the criteria of the existence of blow-up and global existence of solutions. Secondly, we show asymptotic estimates about blow-up time for blow-up solutions and large time estimate for global solutions, respectively.

Key words: p-Kirchhoff pseudo-parabolic equation, Large time estimate, Blow-up time, Initial energy, Variable exponent

中图分类号:

O175.4

李锋杰, 李平. 伪抛物型 p-Kirchhoff 方程的爆破解[J]. 数学物理学报, 2024, 44(3): 717-736.

Li Fengjie, Li Ping. Blow-up Solutions in a p-Kirchhoff Equation of Pseudo-Parabolic Type[J]. Acta mathematica scientia,Series A, 2024, 44(3): 717-736.

图/表 1

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