General decay for a coupled Lamé system of nonlinear viscoelastic equations

Abstract

In this paper, we consider a coupled Lamé system of nonlinear viscoelastic equations with general source terms. Under some suitable conditions on the initial data and the relaxation functions, we prove an asymptotic stability result of global solution taking into account that the kernel is not necessarily decreasing.This work generalizes and improves earlier results in the literature. KEYWORDS coupled system, Lamé system, Lyapunov function, viscoelastic term MSC CLASSIFICATION 35L70; 35B40; 76Exx Δ e u = Δu + ( + ) ∇ (div u) , u = (u 1 , u 2 , u 3 ) T , Math Meth Appl Sci.wileyonlinelibrary.com/journal/mma

Well posedness and stability result for a thermoelastic laminated Timoshenko beam with distributed delay term

“…In the next work, we will apply the distributed delay in our studied problems in previous studies. 18,19,17…”

Global existence and exponential stability of coupled Lamé system with distributed delay and source term without memory term

“…After several authors have studied the problems of coupled systems and hyperbolic systems, their stability is associated with velocities and is proven under some given conditions (see, for example, [1][2][3][4][5][6][7][8][9][10][11]). In recent years, several authors have been interested in studying the existence and stability for Lamé systems, we refer to [12][13][14]. The Lamé system with localized nonlinear damping and a general decay result of energy have been considered by some recent works (see, for example, [12,14], and [15]).…”

“…In recent years, several authors have been interested in studying the existence and stability for Lamé systems, we refer to [12][13][14]. The Lamé system with localized nonlinear damping and a general decay result of energy have been considered by some recent works (see, for example, [12,14], and [15]). Bchatnia et al in [16] investigated Lamé systems with past history.…”

“…They established an explicit and general decay result, which are optimal, to the system. Boulaaras et al in [14] considered the previous problem with a source term, where under some suitable conditions on the initial data and the relaxation functions, they proved an asymptotic stability result of global solution taking into account that the kernel is not necessarily decreasing.…”

General decay and blow-up results of solutions for a viscoelastic wave equation with Robin-Dirichlet conditions

“…It is well known that the single viscoelastic wave equation of the form with initial and boundary conditions, where Ω ⊂ R n is bounded domains with a smooth boundary ∂ Ω, has been extensively studied and many results concerning existence, nonexistence, exponential decay and blow-up in finite time have been proved (see [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15] and references therein).…”