On the General Decay for a System of Viscoelastic Wave Equations

New general decay result for a system of viscoelastic wave equations with past history

“…Our result is obtained under very general assumption on the relaxation functions and without imposing any boundedness condition on the history function u 0 (•, t). Our results generalizes and improves many results in the literature such as [21,18,2,27]…”

“…This latter result allowed a larger class of relaxation functions and generalizes, in some cases, those in [22,25,28]. Very recently, Messaoudi and Hassan [21] considered (1.6) with relaxation functions satisfying g (t) ≤ −ξ(t)H(g(t)), ∀ t ≥ 0 and proved a new general decay result that improves most of the existing results in the literature related to the system of viscoelastic wave equations with finite memory.…”

“…Very recently, Guesmia [12] considered two models of wave equations with infinite memory and established general relations between the decay rate of solutions and the growth of g at infinity. The aim of this work is to investigate problem (P ) with the general class of relaxation functions g 1 and g 2 in the presence of infinite memory terms and use the idea developed by Mustafa in [26,21,12] taking into consideration the difficulty coming from replacing the finite memory with infinite one, to prove a new general decay result. Our result generalizes and improves all the existing results related to system of viscoelastic equations with infinite memories.…”

Stabilization of Weakly Coupled Viscoelastic Kirchhoff Plate and Wave Equations

“…and proved the well-posedness and energy decay result. The decay result was improved by Messaoudi and Hassan in their recent paper [12], where they established a new general decay result for wider class of relaxation functions.…”

“…and proved the well-posedness and energy decay result. The decay result was improved by Messaoudi and Hassan in their recent paper [12], where they established a new general decay result for wider class of relaxation functions. Finally, let us mention the work of Hajej et al [7] in which the authors studied the indirect stabilization (only one equation of the coupled system is damped) of a coupled wave equation and Kirchhoff plate equation without viscoelastic terms ( g 1 = g 2 = 0) and with frictional damping.…”