Global Existence and Blow-up of Solutions for a Class of Singular Parabolic Equations with Viscoelastic Term

Abstract

In this paper, we consider the initial boundary value problem for a class of singular parabolic equations with viscoelastic term and logarithmic term. By using the technique of cut-off and the method of Faedo-Galerkin approximation, the local existence of the weak solution is established. Based on the potential well method, the global existence of the weak solution is derived. Furthermore, we prove that the weak solution blows up in finite time by taking the concavity analysis method.