Initial boundary value problem of a class of pseudo-parabolic Kirchhoff equations with logarithmic nonlinearity

2021/04/04 by Zhao, Qiuting
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2104.01597

Abstract

In this paper, we consider the initial boundary value problem for a pseudo-parabolic Kirchhoff equation with logarithmic nonlinearity. We use the potential well method to give a threshold result of global existence and finite-time blow-up for the weak solutions with initial energy J(u₀)≤ d. When the initial energy J(u₀)>d, we find another criterion for the vanishing solution and blow-up solution. We also get the exponential decay rate of the global solution and life span of the blow-up solution. Meanwhile, we study the corresponding stationary problem and establish a convergence relationship between its ground state solution and the global solution.

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