伪抛物型p-Kirchhoff方程的爆破解  

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

作　　者：李锋杰[1] 李平[1] Li Fengjie;Li Ping(College of Science,China University of Petroleum,Shandong Qingdao 266580)

机构地区：[1]中国石油大学(华东),山东青岛266580

出　　处：《数学物理学报（A辑）》2024年第3期717-736,共20页Acta Mathematica Scientia

基　　金：山东省自然科学基金面上项目(ZR2021MA003)。

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.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.

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 

分 类 号：O175.4[理学—数学]