Fourth order wave equation with nonlinear strain and logarithmic nonlinearity

Abstract

The main goal of this work is to investigate the initial boundary value problem of fourth order wave equation with nonlinear strain and logarithmic nonlinearity at three different initial energy levels, i.e., subcritical energy E(0)<d, critical initial energy E(0)=d and arbitrary high energy E(0)>d. First, we prove the local existence of weak solution by Galerkin method. In the framework of potential well, we obtain the global existence and infinite time blow up of the solution with sub-critical initial energy. Moreover by the scaling technique, we obtain global existence and infinite time blow up of the solution with critical initial energy. Also, a high energy infinite time blow up result is established.