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

摘要

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. (C) 2019 IMACS. Published by Elsevier B.V. All rights reserved.