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Applicable Analysis
An International Journal
Volume 81, 2002 - Issue 6
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Original Articles

Asymptotic Decay for Some Differential Systems with Fading Memory

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Pages 1245-1264 | Published online: 09 Sep 2010

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Read on this site (7)

Muhammad I. Mustafa. (2023) Viscoelasticity versus nonlinear feedback in plate systems: optimal decay. Applicable Analysis 102:15, pages 4140-4161.
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Guilherme F. Tyszka & Higidio Portillo Oquendo. (2023) Indirect stabilization of a coupled system by memory effects. Applicable Analysis 102:9, pages 2591-2610.
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Zhiqing Liu & Zhong Bo Fang. (2022) Optimal decay for a wave transmission problem with fading memory. Applicable Analysis 101:6, pages 1984-2007.
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Ti-Jun Xiao & Hui Zhang. (2018) Optimal decay rates for semilinear wave equations with memory and Neumann boundary conditions. Applicable Analysis 97:15, pages 2594-2609.
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Mohammad M. Al-Gharabli. (2018) A general decay result of a viscoelastic equation with infinite history and nonlinear damping. Applicable Analysis 97:3, pages 382-399.
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Gang Li, Yun Sun & Wenjun Liu. (2014) Arbitrary decay of solutions for a singular nonlocal viscoelastic problem with a possible damping term. Applicable Analysis 93:6, pages 1150-1163.
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Shengqi Yu. (2009) Polynomial stability of solutions for a system of non-linear viscoelastic equations. Applicable Analysis 88:7, pages 1039-1051.
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Articles from other publishers (90)

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Rafael Lima Oliveira, Higidio Portillo Oquendo & Celene Buriol. (2023) Exact decay rates for weakly coupled systems with indirect damping by fractional memory effects. Mathematische Nachrichten.
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Duy Binh Ho, Duc Phuong Nguyen & Viet Tri Vo. (2023) Well-posedness results for a class of nonlinear reaction-diffusion equations with memory. Electronic Journal of Applied Mathematics, pages 1-29.
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Paola F. Antonietti, Lorenzo Liverani & Vittorino Pata. (2023) Lack of superstable trajectories in linear viscoelasticity: a numerical approach. Numerische Mathematik 153:4, pages 611-633.
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Wenhui Chen & Yan Liu. (2023) Asymptotic profiles and singular limits for the viscoelastic damped wave equation with memory of type I. Journal of Mathematical Physics 64:2.
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. (2023) Stability and asymptotic properties of dissipative evolution equations coupled with ordinary differential equations. Mathematical Control and Related Fields 13:1, pages 265-302.
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Houria Chellaoua & Yamna Boukhatem. (2022) General decay for second-order abstract viscoelastic equation in Hilbert spaces with time delay. Boletim da Sociedade Paranaense de Matemática 41, pages 1-18.
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Draifia Alaeddine. (2022) Global existence and general decay of Moore–Gibson–Thompson equation with not necessarily decreasing kernel. Boletim da Sociedade Paranaense de Matemática 41, pages 1-15.
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Muhammad I. Mustafa. (2022) Viscoelastic Timoshenko beams with variable-exponent nonlinearity. Journal of Mathematical Analysis and Applications 516:2, pages 126520.
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Kun-Peng Jin, Jin Liang & Ti-Jun Xiao. (2022) Dynamical behavior of the indirectly and locally memory-damped Timoshenko system. Communications in Nonlinear Science and Numerical Simulation 113, pages 106577.
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Muhammad I. Mustafa. (2022) Optimal Decay Result for Wave Equations with Frictional Versus Viscoelastic Damping. Differential Equations and Dynamical Systems.
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Soh Edwin Mukiawa, McSylvester Ejighikeme Omaba, Cyril Dennis Enyi & Tijani A. Apalara. (2022) General decay estimate for coupled plate problem with memory. Results in Applied Mathematics 15, pages 100306.
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Monica Conti, Filippo Dell'Oro & Vittorino Pata. (2022) Some unexplored questions arising in linear viscoelasticity. Journal of Functional Analysis 282:10, pages 109422.
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Ahlem Merah & Fatiha Mesloub. (2022) Elastic membrane equation with dynamic boundary conditions and infinite memory. Boletim da Sociedade Paranaense de Matemática 40, pages 1-15.
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Jamilu Hashim Hassan & Salim A. Messaoudi. (2021) General decay results for a viscoelastic wave equation with a variable exponent nonlinearity. Asymptotic Analysis 125:3-4, pages 365-388.
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Muhammad I. Mustafa. (2021) Optimal energy decay result for nonlinear abstract viscoelastic dissipative systems. Zeitschrift für angewandte Mathematik und Physik 72:2.
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Houria Chellaoua & Yamna Boukhatem. (2021) Stability results for second-order abstract viscoelastic equation in Hilbert spaces with time-varying delay. Zeitschrift für angewandte Mathematik und Physik 72:2.
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Muhammad I. Mustafa. (2021) On the Control of Dissipative Viscoelastic Timoshenko Beams. Mediterranean Journal of Mathematics 18:2.
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Houria Chellaoua & Yamna Boukhatem. (2020) Optimal decay for second‐order abstract viscoelastic equation in Hilbert spaces with infinite memory and time delay. Mathematical Methods in the Applied Sciences 44:2, pages 2071-2095.
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Huy Tuan Nguyen, Huu Can Nguyen, Renhai Wang & Yong Zhou. (2021) Initial value problem for fractional Volterra integro-differential equations with Caputo derivative. Discrete & Continuous Dynamical Systems - B 26:12, pages 6483.
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Nguyen Huy Tuan, Nguyen Anh Tuan, Donal O’Regan & Vo Viet Tri. (2021) On the initial value problem for fractional Volterra integrodifferential equations with a Caputo–Fabrizio derivative. Mathematical Modelling of Natural Phenomena 16, pages 18.
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Luciano PandolfiLuciano Pandolfi. 2021. Systems with Persistent Memory. Systems with Persistent Memory 223 282 .
Mohammad Shahrouzi. (2021) Global Nonexistence of Solutions for a Class of Viscoelastic Lamé System. Indian Journal of Pure and Applied Mathematics 51:4, pages 1383-1397.
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Filippo Dell’Oro, Irena Lasiecka & Vittorino Pata. (2019) A note on the Moore–Gibson–Thompson equation with memory of type II. Journal of Evolution Equations 20:4, pages 1251-1268.
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Jaime E. Muñoz Rivera, Verónica Poblete, Juan C. Pozo & Octavio Vera. (2019) Asymptotic to systems with memory and non-local initial data. Reviews in Mathematical Physics 32:05, pages 2050014.
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Farida Belhannache, Mohammad M. Algharabli & Salim A. Messaoudi. (2019) Asymptotic Stability for a Viscoelastic Equation with Nonlinear Damping and Very General Type of Relaxation Functions. Journal of Dynamical and Control Systems 26:1, pages 45-67.
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Adel M. Al-Mahdi & Mohammad M. Al-Gharabli. (2019) New general decay results in an infinite memory viscoelastic problem with nonlinear damping. Boundary Value Problems 2019:1.
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Kun-Peng Jin, Jin Liang & Ti-Jun Xiao. (2019) Asymptotic behavior for coupled systems of second order abstract evolution equations with one infinite memory. Journal of Mathematical Analysis and Applications 475:1, pages 554-575.
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Mohammad Shahrouzi. (2018) On behaviour of solutions for a nonlinear viscoelastic equation with variable-exponent nonlinearities. Computers & Mathematics with Applications 75:11, pages 3946-3956.
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Baowei Feng. (2018) General Decay Rates for a Viscoelastic Wave Equation with Dynamic Boundary Conditions and Past History. Mediterranean Journal of Mathematics 15:3.
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Mohammad M. Al-Gharabli & Mohammad M. Kafini. (2017) A general decay result of a coupled system of nonlinear wave equations. Rendiconti del Circolo Matematico di Palermo Series 2 67:1, pages 145-157.
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Shuying Tian. (2017) Bounds for blow-up time in a semilinear parabolic problem with viscoelastic term. Computers & Mathematics with Applications 74:4, pages 736-743.
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Marcelo M. Cavalcanti, Valéria N. Domingos Cavalcanti, Irena Lasiecka & Claudete M. Webler. (2017) Intrinsic decay rates for the energy of a nonlinear viscoelastic equation modeling the vibrations of thin rods with variable density. Advances in Nonlinear Analysis 6:2, pages 121-145.
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Irena Lasiecka. (2016) Global solvability of Moore–Gibson–Thompson equation with memory arising in nonlinear acoustics. Journal of Evolution Equations 17:1, pages 411-441.
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Zhiyong Ma. (2017) Decay Rate for a Viscoelastic Equation with Strong Damping and Acoustic Boundary Conditions. Journal of Applied Mathematics and Physics 05:04, pages 922-932.
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Valéria Neves Domingos Cavalcanti, Irena Lasiecka & Arthur Henrique Caixeta. (2016) On long time behavior of Moore-Gibson-Thompson equation with molecular relaxation. Evolution Equations and Control Theory 5:4, pages 661-676.
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Irena Lasiecka & Xiaojun Wang. (2016) Moore–Gibson–Thompson equation with memory, part I: exponential decay of energy. Zeitschrift für angewandte Mathematik und Physik 67:2.
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Sun-Hye Park. (2016) Arbitrary Decay of Energy for a Viscoelastic Problem with Balakrishnan-Taylor Damping. Taiwanese Journal of Mathematics 20:1.
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Muhammad I. Mustafa. (2014) Uniform Decay Rates for Viscoelastic Dissipative Systems. Journal of Dynamical and Control Systems 22:1, pages 101-116.
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Irena Lasiecka & Xiaojun Wang. (2015) Moore–Gibson–Thompson equation with memory, part II: General decay of energy. Journal of Differential Equations 259:12, pages 7610-7635.
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Serge Nicaise. (2015) Stabilization and asymptotic behavior of a generalized telegraph equation. Zeitschrift für angewandte Mathematik und Physik 66:6, pages 3221-3247.
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Flávio R. Dias Silva, Flávio A. F. Nascimento & José H. Rodrigues. (2015) General decay rates for the wave equation with mixed-type damping mechanisms on unbounded domain with finite measure. Zeitschrift für angewandte Mathematik und Physik 66:6, pages 3123-3145.
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Sun-Hye Park. (2015) Arbitrary decay rates of energy for a von Karman equation of memory type. Computers & Mathematics with Applications 70:8, pages 1878-1886.
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Salim A. Messaoudi & Mohammad M. Al-Gharabli. (2014) A general decay result of a viscoelastic equation with past history and boundary feedback. Zeitschrift für angewandte Mathematik und Physik 66:4, pages 1519-1528.
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Zhifeng Yang. (2014) Existence and energy decay of solutions for the Euler–Bernoulli viscoelastic equation with a delay. Zeitschrift für angewandte Mathematik und Physik 66:3, pages 727-745.
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Salim A. Messaoudi & Mohammad M. Al-Gharabli. (2015) A general decay result of a nonlinear system of wave equations with infinite memories. Applied Mathematics and Computation 259, pages 540-551.
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Marcelo M. Cavalcanti, André D.D. Cavalcanti, Irena Lasiecka & Xiaojun Wang. (2015) Existence and sharp decay rate estimates for a von Karman system with long memory. Nonlinear Analysis: Real World Applications 22, pages 289-306.
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Da Xu. (2014) Decay Properties for the Numerical Solutions of a Partial Differential Equation with Memory. Journal of Scientific Computing 62:1, pages 146-178.
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Wenjun Liu. (2014) Arbitrary rate of decay for a viscoelastic equation with acoustic boundary conditions. Applied Mathematics Letters 38, pages 155-161.
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G. Fiore, A. Maio & P. Renno. (2014) On the initial-value problem in a cold plasma model. Ricerche di Matematica 63:S1, pages 157-164.
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Kun-Peng Jin, Jin Liang & Ti-Jun Xiao. (2014) Coupled second order evolution equations with fading memory: Optimal energy decay rate. Journal of Differential Equations 257:5, pages 1501-1528.
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A. Guesmia & S.A. Messaoudi. (2014) A new approach to the stability of an abstract system in the presence of infinite history. Journal of Mathematical Analysis and Applications 416:1, pages 212-228.
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Sergei A. Avdonin & Boris P. Belinskiy. (2014) On controllability of a linear elastic beam with memory under longitudinal load. Evolution Equations & Control Theory 3:2, pages 231-245.
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Marcelo M. Cavalcanti, Valéria N. Domingos Cavalcanti, Irena Lasiecka & Flávio A. Falcão Nascimento. (2014) Intrinsic decay rate estimates for the wave equation with competing viscoelastic and frictional dissipative effects. Discrete & Continuous Dynamical Systems - B 19:7, pages 1987-2011.
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Irena Lasiecka & Xiaojun Wang. 2014. New Prospects in Direct, Inverse and Control Problems for Evolution Equations. New Prospects in Direct, Inverse and Control Problems for Evolution Equations 271 303 .
Irena Lasiecka, Salim A. Messaoudi & Muhammad I. Mustafa. (2013) Note on intrinsic decay rates for abstract wave equations with memory. Journal of Mathematical Physics 54:3.
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Sergei A. Avdonin & Boris P. Belinskiy. (2013) On controllability of a non-homogeneous elastic string with memory. Journal of Mathematical Analysis and Applications 398:1, pages 254-269.
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Nasser–eddine Tatar. (2012) A New Class of Kernels Leading to an Arbitrary Decay in Viscoelasticity. Mediterranean Journal of Mathematics 10:1, pages 213-226.
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Baowei Feng, Yuming Qin & Ming Zhang. (2012) General decay for a system of nonlinear viscoelastic wave equations with weak damping. Boundary Value Problems 2012:1.
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Fei Liang & Hongjun Gao. (2012) Global existence and blow-up of solutions for a nonlinear wave equation with memory. Journal of Inequalities and Applications 2012:1.
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Nasser‐eddine Tatar. (2012) Oscillating kernels and arbitrary decays in viscoelasticity. Mathematische Nachrichten 285:8-9, pages 1130-1143.
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Serge Nicaise. (2012) Stabilization and asymptotic behavior of dispersive medium models. Systems & Control Letters 61:5, pages 638-648.
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MONICA CONTI, ELSA M. MARCHINI & VITTORINO PATA. (2012) APPROXIMATING INFINITE DELAY WITH FINITE DELAY. Communications in Contemporary Mathematics 14:02, pages 1250012.
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Nasser-eddine Tatar. (2012) Uniform decay in viscoelasticity for kernels with small non-decreasingness zones. Applied Mathematics and Computation 218:15, pages 7939-7946.
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REINHARD RACKE & BELKACEM SAID-HOUARI. (2012) DECAY RATES FOR SEMILINEAR VISCOELASTIC SYSTEMS IN WEIGHTED SPACES. Journal of Hyperbolic Differential Equations 09:01, pages 67-103.
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Muhammad I. Mustafa. (2012) Well posedness and asymptotic behavior of a coupled system of nonlinear viscoelastic equations. Nonlinear Analysis: Real World Applications 13:1, pages 452-463.
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Nasser-Eddine Tatar. (2012) Asymptotic Behavior for a Nondissipative and Nonlinear System of the Kirchhoff Viscoelastic Type. Journal of Applied Mathematics 2012, pages 1-17.
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Shun-Tang Wu. (2011) Arbitrary decays for a viscoelastic equation. Boundary Value Problems 2011:1.
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Mokhtar Kirane & Belkacem Said-Houari. (2011) Existence and asymptotic stability of a viscoelastic wave equation with a delay. Zeitschrift für angewandte Mathematik und Physik 62:6, pages 1065-1082.
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Abdelhak Djebabla & Nasser-eddine Tatar. (2011) Exponential stabilization of the Timoshenko system by a thermal effect with an oscillating kernel. Mathematical and Computer Modelling 54:1-2, pages 301-314.
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Nasser-eddine Tatar. (2011) On a perturbed kernel in viscoelasticity. Applied Mathematics Letters 24:5, pages 766-770.
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Bao-Zhu Guo & Guo-Dong Zhang. (2011) Spectral Analysis and Riesz Basis Property for Wave Equation with Boltzmann Damping. IFAC Proceedings Volumes 44:1, pages 14374-14379.
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Nasser-eddine Tatar. (2011) Arbitrary decays in linear viscoelasticity. Journal of Mathematical Physics 52:1.
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Salim A. Messaoudi & Muhammad I. Mustafa. (2010) On convexity for energy decay rates of a viscoelastic equation with boundary feedback. Nonlinear Analysis: Theory, Methods & Applications 72:9-10, pages 3602-3611.
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Vittorino Pata. (2009) Stability and exponential stability in linear viscoelasticity. Milan Journal of Mathematics 77:1, pages 333-360.
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Nasser-eddine Tatar. (2009) On a large class of kernels yielding exponential stability in viscoelasticity. Applied Mathematics and Computation 215:6, pages 2298-2306.
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Salim A. Messaoudi & Muhammad Islam Mustafa. (2009) On the control of solutions of viscoelastic equations with boundary feedback. Nonlinear Analysis: Real World Applications 10:5, pages 3132-3140.
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Mohammad Kafini & Salim A. Messaoudi. (2009) On the uniform decay in viscoelastic problems in. Applied Mathematics and Computation 215:3, pages 1161-1169.
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