Local Existence and Blow up for a Nonlinear Viscoelastic Kirchhoff-type Equation with Logarithmic Nonlinearity

Abstract

The aim of this paper is to consider the initial boundary value problem of nonlinear viscoelastic Kirchhoff-type equation with logarithmic source term. Firstly, we prove the local existence of weak solution by applying Banach fixed theorem. Later, we derive the blow-up results by the combination of the perturbation energy method, concavity method and differential-integral inequality technique.