References
- A.C. Lazer and P.J. McKenna, Large-amplitude periodic oscillations in suspension bridge: some new connections with nonlinear analysis, SIAM REV. 32 (1990), 537-578. https://doi.org/10.1137/1032120
- I. Chueshov and I.Lasiecka, Von Karman Evolution Equations: Well-Posedness and Long-Time Dynamics, Springer Monographs in Mathematics, Springer, New York, 2010.
- C.K. Zhong, Q.Z. Ma and C.Y. Sun, Existence of strong solutions and global attractors for the suspension bridge equations, Nonlinear Anal. 67 (2007), 442-454. https://doi.org/10.1016/j.na.2006.05.018
- J.R. Kang, Pullback attractors for the non-autonomous coupled suspension bridge equations, Appl. Math. Comput. 219 (2013), 8747-8758.
- Q.Z. Ma and C.K. Zhong, Existence of global attractors for the coupled system of suspension bridge equations, J. Math. Anal. Appl, 308 (2005), 365-379. https://doi.org/10.1016/j.jmaa.2005.01.036
- Q.Z. Ma and C.K. Zhong, Existence of strong solutions and global attractors for the coupled suspension bridge equations, J. Diff. Equ. 246 (2009), 3755-3775. https://doi.org/10.1016/j.jde.2009.02.022
- Q.Z. Ma, S.P. Wang and X.B. Chen, uniform compact attractors for the coupled suspension bridge equations, Appl. Math. Comput. 15 (2011), 6604-6615.
- J.Y. Park and J.R. Kang, Pullback D-attractors for non-autonomous suspension bridge equations, Nonlinear Anal. 71 (2009), 4618-4623. https://doi.org/10.1016/j.na.2009.03.025
- J.Y. Park and J.R. Kang, Global attractor for suspension bridge equation with nonlinear damping, Quart. Appl. Math. 69 (2011), 465-475. https://doi.org/10.1090/S0033-569X-2011-01259-1
- L. Xu and Q.Z. Ma, Existence of random attractors for the floating beam equation with strong damping and white noise, Boundry Value Problem. 126 (2015), 1-13.
- J.M. Ball, Initial-boundary value problems for an extensible beam, J. Math. Anal. Appl. 42 (1973), 61-90. https://doi.org/10.1016/0022-247X(73)90121-2
- J.M. Ball, Stability theory for an extensible beam, J. Diff. Equ. 14 (1973), 399-418. https://doi.org/10.1016/0022-0396(73)90056-9
- I. Bochicchio, C. Giorgi and E. Vuk, Long-term damped dynamics of the extensible suspension bridge, Int. J. Diff. Equ. 10 (2010), 1155-1174.
- Q.Z. Ma and L. Xu, Random attractors for the extensible suspension bridge equation with white noise, Comput. Math. Appl. 70 (2015), 2895-2903. https://doi.org/10.1016/j.camwa.2015.09.029
- J.R. Kang, Long-time behavior of a suspension bridge equations with past history, Appl. Math. Comput. 265 (2015), 509-519
- M. Fabrizio, C. Giorgi and V. Pata, A new approach to equations with memory, Arch. Ration, Mech. Anal. 198 (2010), 189-232. https://doi.org/10.1007/s00205-010-0300-3
- V. Pata and A. Zucchi, Attractors for a damped hyperbolic equation with linear memory, Math. Sci. Appl. 2 (2001), 505-529.
- J.Y. Park and J.R. Kang, Global attractor for hyperbolic equation with nonlinear damping and linear memory, Sci. China Math. 53 (6) (2010), 1531-1539. https://doi.org/10.1007/s11425-010-3110-z
- R. Temam, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Appl. Math. Sci, Vol. 68, Springer-Verlag, New York, 1988.