General and optimal decay for a quasilinear viscoelastic equation

General decay rate for a class of weakly dissipative second‐order systems with memory

“…() In the case of finite history, that is, u 0 ( t ) = 0 for t < 0, see Berrimi and Messaoudi, Messaoudi, Messaoudi and Al‐Khulaifi, Muñoz Rivera et al, and Mustafa. () In particular, Rivera et al considered the interpolating cases α ∈ (0,1) and a relaxation function g , which decay exponentially to 0 at infinity, that is, …”

Blow-Up and Global Existence Analysis for the Viscoelastic Wave Equation with a Frictional and a Kelvin-Voigt Damping

“…In [4] in Ω, (2) and he proved, under certain additional restrictions on the relaxation function , that the energy of IBVP (2) decreases to zero. The results and methods in [4] were later extended by Messaoudi and Al-Khulaifi [5] (3) more precisely, they established some general decay results for IBVP (3). It was shown in both [4,5] that the energy decay rate is closely related to the peculiarity of the relaxation function .…”

“…The results and methods in [4] were later extended by Messaoudi and Al-Khulaifi [5] (3) more precisely, they established some general decay results for IBVP (3). It was shown in both [4,5] that the energy decay rate is closely related to the peculiarity of the relaxation function . Different from (2) 1 , the wave speed of (3) 1 depends on the velocity of the wave.…”

Optimal decay result for Kirchhoff plate equations with nonlinear damping and very general type of relaxation functions

“…Using the above condition and imposing additional constraints conditions on G, several authors in different approaches obtained general decay results in terms of G; see for example [32][33][34][35][36], and [37]. Later, the condition (6) was extended by Messaoudi and Al-Khulaifi [38] to the case 1 ≤ p < 3 2 only and they obtained general and optimal decay results. In [34], Lasiecka et al established optimal decay rate for all 1 ≤ p < 2, but with γ (t) = 1.…”