伪抛物型 p-Kirchhoff 方程的爆破解

Abstract

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

CLC Number:

O175.4

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.

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

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