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

Aounallah Radhouane, Choucha Abdelbaki, Boulaaras Salah, Zarai Abderrahmane

Archives of Control Sciences

2024

Vol. 34, No. 2

379--413

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.