[1] Abouelregal A E, Zenkour A M. Thermoelastic problem of an axially moving microbeam subjected to an external transverse excitation. J Theor App Mech, 2015, 53(1):167-178 [2] Avsec J, Oblak M. Thermal vibrational analysis for simply supported beam and clamped beam. J Sound Vib, 2007, 308(3):514-525 [3] Babin A V, Vishik M I. Attractors of evolution equations, translated and revised from the 1989 Russian original by Babin, Studies in Mathematics and its Applications, 25. Amsterdam:North-Holland Publishing Co, 1992 [4] Barbosa A R A, Ma T F. Long-time dynamics of an extensible plate equation with thermal memory. J Math Anal Appl, 2014, 416(1):143-165 [5] Boulanouar F, Drabla S. General boundary stabilization result of memory-type thermoelasticity with second sound. Electron J Differential Equations, 2014, 2014(202):18 pp [6] Brezis H. Functional analysis, Sobolev spaces and partial differential equations//Universitext. New York:Springer, 2011 [7] Chen D Q, Liu W J, Chen Z J. General decay for a thermoelastic problem of a microbeam with GurtinPipkin thermal law (submitted) [8] Chepyzhov V V, Pata V. Some remarks on stability of semigroups arising from linear viscoelasticity. Asymptot Anal, 2006, 46(3/4):251-273 [9] Chueshov I, Lasiecka I. Long-time behavior of second order evolution equations with nonlinear damping. Mem Amer Math Soc, 2008, 195(912):viii+183 pp [10] Chueshov I, Lasiecka I. Von Karman evolution equations. Springer Monographs in Mathematics. New York:Springer, 2010 [11] Coleman B D, Gurtin M E. Equipresence and constitutive equations for rigid heat conductors. Z Angew Math Phys, 1967, 18:199-208 [12] Conti M,Marchini E M, Pata V. Global attractors for nonlinear viscoelastic equations with memory. Commun Pure Appl Anal, 2016, 15(5):1893-1913 [13] Dafermos C M. Asymptotic stability in viscoelasticity. Arch Rational Mech Anal, 1970, 37:297-308 [14] Díaz R, Vera O. Asymptotic behaviour for a thermoelastic problem of a microbeam with thermoelasticity of type Ⅲ. Electron J Qual Theory Differ Equ, 2017, 2017(74):13 pp [15] Fatori L H, et al. Long-time behavior of a class of thermoelastic plates with nonlinear strain. J Differential Equations, 2015, 259(9):4831-4862 [16] Feng B. On a semilinear Timoshenko-Coleman-Gurtin system:quasi-stability and attractors. Discrete Contin Dyn Syst, 2017, 37(9):4729-4751 [17] Feng B, Pelicer M L. Global existence and exponential stability for a nonlinear Timoshenko system with delay. Bound Value Probl, 2015, 2015(206):13 pp [18] Fridman E. Introduction to time-delay systems. Systems & Control:Foundations & Applications. Cham:Birkhäuser/Springer, 2014 [19] Gatti S, et al. Attractors for semi-linear equations of viscoelasticity with very low dissipation. Rocky Mountain J Math, 2008, 38(4):1117-1138 [20] Giorgi C, Pata V, Marzocchi A. Asymptotic behavior of a semilinear problem in heat conduction with memory. NoDEA Nonlinear Differential Equations Appl, 1998, 5(3):333-354 [21] Grasselli M, Muñoz Rivera J E, Pata V. On the energy decay of the linear thermoelastic plate with memory. J Math Anal Appl, 2005, 309(1):1-14 [22] Grasselli M, Pata V. Uniform attractors of nonautonomous dynamical systems with memory//Evolution equations, semigroups and functional analysis. Milano, 2000:155-178; Progr Nonlinear Differential Equations Appl, 50. Basel:Birkhäuser, 2002 [23] Hale J K. Asymptotic behavior of dissipative systems. Mathematical Surveys and Monographs, 25. Providence, RI:American Mathematical Society, 1988 [24] Hale J K, Verduyn Lunel S M. Introduction to functional-differential equations//Applied Mathematical Sciences, 99. New York:Springer-Verlag, 1993 [25] Hao J H, Wang F. General decay rate for weak viscoelastic wave equation with Balakrishnan-Taylor damping and time-varying delay. Comput Math Appl, 2019, 78(8):2632-2640 [26] Hao J H, Wei J. Global existence and stability results for a nonlinear Timoshenko system of thermoelasticity of type Ⅲ with delay. Bound Value Probl, 2018, Paper No. 65, 17 pp [27] Houston B H, Photiadis D M, Vignola J F, et al. Loss due to transverse thermoelastic currents in microscale resonators. Materials Science & Engineering A, 2004, 370(1):407-411 [28] Komornik V. Exact controllability and stabilization. RAM:Research in Applied Mathematics. Paris:Masson, 1994 [29] Kirane M, Said-Houari B. Existence and asymptotic stability of a viscoelastic wave equation with a delay. Z Angew Math Phys, 2011, 62(6):1065-1082 [30] Kirane M, Said-Houari B, Anwar M N. Stability result for the Timoshenko system with a time-varying delay term in the internal feedbacks. Commun Pure Appl Anal, 2011, 10(2):667-686 [31] Ladyzhenskaya O. Attractors for semigroups and evolution equations. Lezioni Lincee, Cambridge:Cambridge University Press, 1991 [32] Liu G, Yue H, Zhang H. Long time behavior for a wave equation with time delay. Taiwanese J Math, 2017, 21(1):107-129 [33] Liu W J, Chen K W, Yu J. Existence and general decay for the full von Kármán beam with a thermoviscoelastic damping, frictional dampings and a delay term. IMA J Math Control Inform, 2017, 34(2):521-542 [34] Liu W J, Chen K W, Yu J. Asymptotic stability for a non-autonomous full von Kármán beam with thermoviscoelastic damping. Appl Anal, 2018, 97(3):400-414 [35] Liu W J, Zhao W F. Stabilization of a thermoelastic laminated beam with past history. Appl Math Optim, 2019, 80(1):103-133 [36] Messaoudi S A, Fareh A. General decay for a porous-thermoelastic system with memory:the case of nonequal speeds. Acta Mathematica Scientia, 2013, 33B(1):23-40 [37] Nicaise S, Pignotti C. Stability and instability results of the wave equation with a delay term in the boundary or internal feedbacks. SIAM J Control Optim, 2006, 45(5):1561-1585 [38] Nicaise S, Valein J, Fridman E. Stability of the heat and of the wave equations with boundary time-varying delays. Discrete Contin Dyn Syst Ser S, 2009, 2(3):559-581 [39] Pazy A. Semigroups of linear operators and applications to partial differential equations//Applied Mathematical Sciences, 44. New York:Springer-Verlag, 1983 [40] Potomkin M. Asymptotic behavior of thermoviscoelastic Berger plate. Commun Pure Appl Anal, 2010, 9(1):161-192 [41] Qin Y, Ren J, Wei T. Global existence, asymptotic stability, and uniform attractors for non-autonomous thermoelastic systems with constant time delay. J Math Phys, 2012, 53(6):063701, 20 pp [42] Temam R. Infinite-dimensional dynamical systems in mechanics and physics//Applied Mathematical Sciences, 68. New York:Springer-Verlag, 1988 [43] Vera O, Rambaud A, Rozas R. Stabilization of transverse vibrations of an inhomogeneous Euler-Bernoulli beam with a thermal effect. arXiv:1506.01659v2 [44] Xu G Q, Yung S P, Li L K. Stabilization of wave systems with input delay in the boundary control. ESAIM Control Optim Calc Var, 2006, 12(4):770-785 [45] Zhang Q. Stability analysis of an interactive system of wave equation and heat equation with memory. Z Angew Math Phys, 2014, 65(5):905-923 |