2019
DOI: 10.1002/mma.5998
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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 + … Show more

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Cited by 12 publications
(11 citation statements)
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“…In the next work, we will apply the distributed delay in our studied problems in previous studies. 18,19,17…”
Section: Resultsmentioning
confidence: 99%
“…In the next work, we will apply the distributed delay in our studied problems in previous studies. 18,19,17…”
Section: Resultsmentioning
confidence: 99%
“…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]).…”
Section: Introductionmentioning
confidence: 99%
“…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.…”
Section: Introductionmentioning
confidence: 99%
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“…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).…”
Section: Introductionmentioning
confidence: 99%