Blow up and asymptotic behavior for a system of viscoelastic wave equations of Kirchhoff type with a delay term

Abstract

The focus of the current paper is to investigate the initial boundary value problem for a system of viscoelastic wave equations of Kirchhoff type with a delay term in a bounded domain. At first, the energy decay rate is proved by Nakao’s technique and expressed polynomially and exponentially depending on the parameter m. However and in the unstable set, for certain initial data, the blow up of solutions is obtained

Keywords

• Global existence
• Energy decay
• Blow up of solutions
• Nonlinear damping