Qualitative analysis of solutions for a class of Kirchhoff equation with linear strong damping term, nonlinear weak damping term and power-type logarithmic source term

Abstract

In this paper, we study the initial boundary value problem for Kirchhoff equation with linear strong damping term, nonlinear weak damping term and power-type logarithmic source term at three different initial energy levels, i.e. subcritical energy E(0)<d, critical initial energy E(0)=d and the arbitrary high energy E(0)>0. By potential well method, we prove global existence, finite time blow up and asymptotic behavior of solutions in cases of E(0)<d and E(0)=d. We also prove the finite time blow up of solutions to the problem with linear weak and strong damping term in the case of E(0)>0.