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General decay rate of a weakly dissipative viscoelastic equation with a general damping

100%

Khaleel A. , Messaoudi S. A.

Opuscula Mathematica

2020

tom Vol. 40, no. 6

647–-666

In this paper, we consider a weakly dissipative viscoelastic equation with a nonlinear damping. A general decay rate is proved for a wide class of relaxation functions. To support our theoretical findings, some numerical results are provided.

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

88%

Aounallah R. , Choucha A. , Boulaaras S. , Zarai A.

Archives of Control Sciences

2024

tom 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.

Decay rates for a coupled quasilinear system of nonlinear viscoelastic equations

63%

Mustafa M. I. , Kafini M.

Journal of Applied Analysis

2019

tom Vol. 25, nr 1

97--110

In this paper, we consider a nonlinear quasilinear system of two coupled viscoelastic equations and investigate the asymptotic behavior of this system. We establish an explicit and general formula for the energy decay rates. Our result allows a wider class of relaxation functions, which improves earlier results existing in the literature.