伪抛物型p-Kirchhoff方程的爆破解

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

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.