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Global existence and exponential decay for a viscoelastic equation with not necessarily decreasing kernel

Alaeddine Draifia

Journal of Applied Analysis

2022

Vol. 28, nr 2

219--236

In this paper, we consider the nonlinear viscoelastic equation utt − Δu + t∫0h(t − s)Δu(s) ds + a(x)|ut|mut + |u|γu = 0 in a bounded domain with kernels not necessarily exponentially decaying to zero and we obtain an asymptotic stability result of global solutions.

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

Khaleel Anaya, Messaoudi Salim A

Opuscula Mathematica

2020

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.

Decay rates for a coupled quasilinear system of nonlinear viscoelastic equations

Mustafa Muhammad I., Kafini Mohammad

Journal of Applied Analysis

2019

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.