[1] COLEMAN, B. D. and NOLL, W. Foundations of linear viscoelasticity. Reviews of Modern Physics, 33, 239-249(1961)
[2] COLEMAN, B. D. and MIZEL, V. J. On the general theory of fading memory. Archive for Rational Mechanics and Analysis, 29, 18-31(1968)
[3] FABRIZIO, M. and MORRO, A. Mathematical problems in linear viscoelasticity. Mathematical Problems in Linear Viscoelasticity, Society for Industrial and Applied Mathematics Philadelphia, Pennsylvania (1992)
[4] GE, S. S., HE, W., HOW, B. V. E., and CHOO, Y. S. Boundary control of a coupled nonlinear exible marine riser. IEEE Transactions on Control Systems and Technology, 18, 1080-1091(2010)
[5] HE, W., GGE, S. S., and ZHANG, S. Adaptive boundary control of a exible marine installation system. Automatica, 47, 2728-2734(2011)
[6] HE, W., ZHANG, S., and GE, S. S. Boundary control of a exible riser with the application to marine installation. Transactions on Industrial Electronics, 60, 5802-5810(2013)
[7] NQUYEN, T. L., DO, K. D., and PAN, J. Boundary control of coupled nonlinear three dimensional marine risers. Journal of Marine Sciences and Application, 12, 72-88(2013)
[8] PARK, J. Y., KANQ, H. K., and KIM, J. A. Existence and exponential stability for a EulerBernoulli beam equation with memory and boundary output feedback control term. Acta Applicandae Mathematicae, 104, 287-301(2008)
[9] LAZZARI, B. and NIBBI, R. On the exponential decay of the Euler-Bernoulli beam with boundary energy dissipation. Journal of Mathematical Analysis and Applications, 389, 1078-1085(2012)
[10] KANG, Y. H., PARK, J. Y., and KIM, J. A. A memory type boundary stabilization for an EulerBernoulli beam under boundary output feedback control. Journal of the Korean Mathematical Society, 49, 947-964(2012)
[11] CAVALCANTI, M. M. Existence and uniform decay for the Euler-Bernoulli viscoelastic equation with nonlocal boundary dissipation. Discrete and Continuous Dynamical Systems, 8, 675-695(2002)
[12] CAVALCANTI, M. M., DOMINGOS-CAVALCANTI, V. N., and MA, T. F. Exponential decay of the viscoelastic Euler-Bernoulli equation with a nonlocal dissipation in general domains. Differential and Integral Equations, 17, 495-510(2004)
[13] CAVALCANTI, M. M., DOMINGOS-CAVALCANTI, V. N., and SORIANO, J. A. Global existence and asymptotic stability for the nonlinear and generalized damped extensible plate equation. Communications in Contemporary Mathematics, 6, 705-731(2004)
[14] CAVALCANTI, M. M., DOMINGOS-CAVALCANTI, V. N., and FERREIRA, J. Existence and uniform decay for a non-linear viscoelastic equation with strong damping. Mathematical Methodes in the Applied Sciences, 24, 1043-1053(2001)
[15] CAVALCANTI, M. M., DOMINGOS-CAVALCANTI, V. N., and MARTINAZ, P. General decay rate estimates for viscoelastic dissipative systems. Nonlinear Analysis:Theory, Methods & Applications, 68, 177-193(2008)
[16] BERKANI, A., TATAR, N. E., and KHEMMOUDJ, A. Control of a viscoelastic translational Euler-Bernoulli beam. Mathematical Methodes in the Applied Sciences, 40, 237-254(2017)
[17] SEGHOUR, L., KHEMMOUDJ, A., and TATAR, N. E. Control of a riser through the dynamic of the vessel. Applicable Analysis, 95, 1957-1973(2016)
[18] KELLECHE, A., TATAR, N. E., and KHEMMOUDJ, A. Uniform stabilization of an axially moving Kirchhoff string by a boundary control of memory type. Journal of Dynamical Control Systems, 23, 237-247(2016)
[19] KELLECHE, A., TATAR, N. E., and KHEMMOUDJ, A. Stability of an axially moving viscoelastic beam. Journal of Dynamical Control Systems, 23, 283-299(2017)
[20] ZHANG, Z. Y., MIAO, X. J., and YU, D. On solvability and stabilization of a class of hyperbolic hemivariational inequalities in elasticity. Funkcialaj Ecvacioj, 54, 297-314(2011)
[21] ZHANG, Z. Y. and HUANG, J. On solvability of the dissipative Kirchhoff equation with nonlinear boundary damping. Bulletin Korean Mathematical Society, 51, 189-206(2014)
[22] ZHANG, Z. Y. and MIAO, X. J. Global existence and uniform decay for wave equation with dissipative term and boundary damping. Computers and Mathematics with Applications, 59, 1003-1018(2010)
[23] KOMORNIK, V. and ZUAZUA, E. A direct method for boundary stabilization of the wave equation. Journal de Mathématiques Pures et Appliquées, 69, 33-54(1990)
[24] ZHANG, Z. Y., LIU, Z. H., MIAO, X. J., and CHEN, Y. Z. Stability analysis of heat flow with boundary time-varying delay effect. Nonlinear Analysis, 73, 1878-1889(2010)
[25] ZHANG, Z. Y., LIU, Z. H., MIAO, X. J., and CHEN, Y. Z. A note on decay properties for the solutions of a class of partial differential equation with memory. International Journal of Applied Mathematics and Computer, 37, 85-102(2011)
[26] ZHANG, Z. Y., LIU, Z. H., MIAO, X. J., and CHEN, Y. Z. Global existence and uniform stabilization of a generalized dissipative Klein-Gordon equation type with boundary damping. Journal of Mathematical Physics, 52, 023502(2011)
[27] DAFERMOS, C. M. On abstract Volterra equations with applications to linear viscoelasticity. Journal of Differential Equations, 7, 554-569(1970)
[28] DAFERMOS, C. M. Asymptotic stability in viscoelasticity. Archive for Rational Mechanics and Analysis, 37, 297-308(1970)
[29] JIN, K. P., LIANG, J., and XIAO, T. J. Coupled second order evolution equations with fading memory:optimal energy decay rate. Journal of Differential Equations, 257, 1501-1528(2014)
[30] BERRIMI, S. and MESSAOUDI, S. A. Existence and decay of solutions of a viscoelastic equation with a nonlinear source. Nonlinear Analysis, 64, 2314-2331(2006)
[31] CABANILLAS, E. L. and MUNOZ-RIVERA, J. E. Decay rates of solutions of an anisotropic inhomogeneous n-dimensional viscoelastic equation with polynomial decaying kernels. Communications in Mathematical Physics, 177, 583-602(1996)
[32] HRUSA, W. J. Global existence and asymptotic stability for a semilinear Volterra equation with large initial data. SIAM Journal of Mathematical Analysis, 16, 110-134(1985)
[33] MESSAOUDI, S. A. and TATAR, N. E. Global existence and uniform stability of solutions for a quasilinear viscoelastic problem. Mathematical Methodes in the Applied Sciences, 30, 665-680(2007)
[34] MUNOZ-RIVERA, J. E. Asymptotic behavior in linear viscoelasticity. Quarterly of Applied Mathematics, 52(4), 628-648(1994)
[35] ALABAU-BOUSSOUIRA, F., CANNARSA, P., and SFORZA, D. Decay estimates for the second order evolution equation with memory. Journal of Functional Analysis, 245, 1342-1372(2008)
[36] CANNARSA, P. and SFORZA, D. Integro-differential equations of hyperbolic type with positive definite kernels. Journal of Differential Equations, 250, 4289-4335(2011)
[37] MUNOZ-RIVERA, J. E. and NASO, M. G. On the decay of the energy for systems with memory and indefinite dissipation. Asymptotic Analysis, 49, 189-204(2006)
[38] MUNOZ-RIVERA, J. E., NASO, M. G., and VEGNI, F. M. Asymptotic behavior of the energy for a class of weakly dissipative second-order systems with memory. Journal of Mathematical Analysis and Applications, 286, 692-704(2003)
[39] CAVALCANTI, M. M., DOMINGOS-CAVALCANTI, V. N., and FERREIRA, J. Existence and uniform decay for nonlinear viscoelastic equation with strong damping. Mathematical Methodes in the Applied Sciences, 24, 1043-1053(2001)
[40] MESSAOUDI, S. A. General decay of solutions of a viscoelastic equation. Journal of Mathematical Analysis and Applications, 341, 1457-1467(2008)
[41] MESSAOUDI, S. A. General decay of the solution energy in a viscoelastic equation with a nonlinear source. Nonlinear Analysis, 69, 2589-2598(2008)
[42] HAN, X. I. and WANG, M. General decay of energy for a viscoelastic equation with nonlinear damping. Mathematical Methodes in the Applied Sciences, 32, 346-358(2009)
[43] LIU, W. J. General decay rate estimate for a viscoelastic equation with weakly nonlinear timedependent dissipation and source terms. Journal of Mathematical Physics, 50, 113506(2009)
[44] LIU, W. J. General decay and blow-up of solution for a quasilinear viscoelastic problem with nonlinear source. Nonlinear Analysis, 73, 1890-1904(2010)
[45] LASIECKA, I. and TATARU, D. Uniform boundary stabilization of semilinear wave equation with nonlinear boundary damping. Differential and Integral Equations, 8, 507-533(1993)
[46] ALABAU-BOUSSOUIRA, F. and CANNARSA, P. A general method for proving sharp energy decay rates for memory-dissipative evo-lution equations. Comptes Rendus de l'Académie des Sciences Paris, Serie I, 347, 867-872(2009)
[47] MUSTAFA, M. I. and MESSAOUDI, S. A. General stability result for viscoelastic wave equations. Journal of Mathematical Physics, 53, 053702(2012)
[48] CAVALCANTI, M. M., CAVALCANTI, A. N. D., LASIECKA, I., and WANG, X. Existence and sharp decay rate estimates for a von Karman system with long memory. Nonlinear Analysis Real World Applications, 22, 289-306(2015)
[49] CAVALCANTI, M. M., CAVALCANTI, A. N. D., LASIECKA, I., and Nascimento, F. A. Intrinsic decay rate estimates for the wave equation with competing viscoelastic and frictional dissipative effects. Discrete and Continuous Dynamical Systems. Series B, 19, 1987-2012(2014)
[50] CAVALCANTI, M. M., CAVALCANTI, A. N. D., LASIECKA, I., and WEBLER, C. M. 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, 121-145(2017)
[51] GUESMIA, A. Asymptotic stability of abstract dissipative systems with infinite memory. Journal of Mathematical Analysis and Applications, 382, 748-760(2011)
[52] LASIECKA, I., MESSAOUDI, S. A., and MUSTAFA, M. I. Note on intrinsic decay rates for abstract wave equations with memory. Journal of Mathematical Physics, 54, 031504(2013)
[53] LASIECKA, I. and WANG, X. Intrinsic decay rate estimates for semilinear abstract second order equations with memory. New Prospects in Direct, Inverse and Control Problems for Evolution Equations, Springer, Chambridge (2014)
[54] MESSAOUDI, S. A. General decay of solutions of a viscoelastic equation. Journal of Mathematical Analysis and Applications, 341, 1457-1467(2008)
[55] MESSAOUDI, S. A. General decay of the solution energy in a viscoelastic equation with a nonlinear source. Nonlinear Analysis, 69, 2589-2598(2008)
[56] DO, K. D. and PAN, J. Boundary control of transverse motion of marine risers with actuator dynamics. Journal of Sound and Vibration, 318, 768-791(2008)
[57] HARDY, G. H., LITTLEWOOD, J. E., and POLYA, G. Inequalities, Cambridge University Press, Cambridge (1959)
[58] RAHN, C. D. Mechantronic Control of Distributed Noise and Vibration, Springer, New York (2001)
[59] AUBIN, J. P. Un théorème de compacité. Comptes Rendus de l'Acadéie des Sciences Paris, 256, 5042-5044(1963)
[60] LIONS, J. L. Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires, Dunod, Paris (1969)
[61] ZHENG, S. Nonlinear evolution equations. Pitman series Monographs and Survey in Pure and Applied Mathematics, Chapman & Hall/CRC, Boca Raton (2004)
[62] ARARUNA, F. D., BRAZ, E., SILVA, P., and ZUAZUA, E. Asymptotic limits and stabilization for the 1d nonlinear Mindlin-Timoshenko system. Journal of Systems Science and Complexity, 23, 1-17(2010)
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