Global existence and exponential stability of coupled Lamé system with distributed delay and source term without memory term

Abstract

Abstract In this paper, we prove the global existence and exponential energy decay results of a coupled Lamé system with distributed time delay, nonlinear source term, and without memory term by using the Faedo–Galerkin method. In addition, an appropriate Lyapunov functional, more general relaxation functions, and some properties of convex functions are considered.

Keywords

• Viscoelastic term
• Delay function
• Lyapunov functional
• Distributed delay
• Exponential decay