Asymptotic behavior of a viscoelastic wave equation with a delay in internal fractional feedback

Abstract

We consider the viscoelastic wave equation with a time delay term in internal fractional feedback. By employing the energy method along with the Faedo-Galerkin procedure, we establish the global existence of solutions, subject to certain conditions. Additionally, we demonstrate how appropriate Lyapunov functionals can lead to general decay results of the energy.

Keywords

• global existence
• general decay
• relaxation function
• delay fractional feedback
• partial differential equations