Uniform attractors of non-autonomous suspension bridge equations with memory
DOI:
https://doi.org/10.58997/ejde.2024.16Abstract
In this article, we investigate the long-time dynamical behavior of non-autonomous suspension bridge equations with memory and free boundary conditions. We first establish the well-posedness of the system by means of the maximal monotone operator theory. Secondly, the existence of uniformly bounded absorbing set is obtained. Finally, asymptotic compactness of the process is verified, and then the existence of uniform attractors is proved for non-autonomous suspension bridge equations with memory term.
For more information see https://ejde.math.txstate.edu/Volumes/2024/16/abstr.html
References
N. U. Ahmed, H. Harbi; Mathematical analysis of dynamical models of suspension bridge, SIAM J. Appl. Math., 58 (1998), 853-874.
M. Al-Gwaiz, V. Benci, F. Gazzola; Bending and stretching energies in a rectangular plate modeling suspension bridges, Nonlinear Anal., 106 (2014), 18-34.
I. Bochicchio, C. Giorgi, E. Vuk; Long-term damped dynamics of the extensible suspension bridge equations, Inter. J. Diff. Equ., 2010 (2010), 1-19.
E. Berchio, F. Gazzola; A qualitative explanation of the origin of torsional instability in suspension bridges, Nonlinear Anal., 121 (2015), 54-72.
E. Berchio, A. Ferrero, F. Gazzola; Structural instability of nonlinear plates modeling suspension bridges: mathematical answers to some long-standing questions, Nonlinear Anal. Real World Appl., 28 (2016), 91-125.
I. Chueshov, I. Lasiecka; Von Karman Evolution Equations: Well-posedness and Long-time Dynamics. Springer Monographs in Mathematics, Springer, New York, 2010.
V. V. Chepyzhov, M. I. Vishik; Attractors for Equations of Mathematical Physics. American Mathematical Society Colloquium Publications, vol 49. Am Math. Soc, Providence, 2002.
C. M. Dafermos; Asymptotic stability in viscoelasticity, Arch. Rational Mech. Annl., 37 (1970), 297-308.
A. Ferrero, F. Gazzola; A partially hinged rectangular plate as a model for suspension bridge, Discrete Contin. Dyn. Syst., 35 (2015), 5879-5908.
B. W. Feng, X. G. Yang, Y. M. Qin; Uniform attractors for a nonautonomous extensible plate equation with a strong damping, Math. Meth. Appl. Sci., 40 (2017), 3479-3492.
F. Gazzola; Mathematical Models for Suspension Bridges: Nonlinear Structural Instability, Modeling, Simulation and Applications. Vol. 15, Springer-Verlag, 2015.
Z. Hajjej; General decay of solutions for a viscoelastic suspension bridge with nonlinear damping and a source term, Z. Angew. Math. Phys., 72 (2021), 1-26.
Z. Hajjej, M. M. Al-Gharabli, S. A. Messaoudi; Stability of a suspension bridge with a localized structural damping, Discrete Contin. Dyn. Syst. S., 15 (2022), 1165-1181.
J. R. Kang; Global attractor for suspension bridge equations with memory, Math. Methods Appl. Sci., 39 (2016), 762-775.
A. C. Lazer, P. J. McKenna; Large scale oscillatory behaviour in loaded asymmetric systems, Ann. Inst. H. PoincarŽe Anal. Non LinŽeaire., 4 (1987), 243-274.
A. C. Lazer, P. J. Mckenna; Large-amplitude periodic oscillations in suspension bridges: Some new connections with nonlinear analysis, SIAM Rev., 32 (1990), 537-578.
P. J. McKenna, W. Walter; Nonlinear oscillations in a suspension bridge, Arch. Rational Mech. Anal., 98 (1987), 167-177.
Q. Z. Ma, C. K. Zhong; Existence of global attractors for the coupled system of suspension bridge equations, J. Math. Anal. Appl., 308 (2005), 365-379.
Q. Z. Ma, C. K. Zhong; Existence of global attractors for the suspension bridge equations, J. Sichuan Normal Univ. Nat. Sci., 43 (2006), 271-276.
Q. Z. Ma, C. K. Zhong; Existence of strong solutions and global attractors for the coupled suspension bridge equations, J. Diff. Equ., 246 (2009), 3755-3775.
Q. Z. Ma, S. P. Wang, X. B. Chen; Uniform compact attractors for the coupled suspension bridge equations, Appl. Math. Comput., 217 (2011), 6604-6615.
S. A. Messaoudi, S. E. Mukiawa; Existence and decay of solutions to a viscoelastic plate equation, Electron. J. Diff. Equ., 22 (2016), 1-14.
S. A. Messaoudi, A. Bonfoh, S. E. Mukiawa, C. D. Enyi; The global attractor for a suspension bridge with memory and partially hinged boundary conditions, Z. Angew. Math. Mech., 97 (2016), 1-14.
S. Mukiawa, M. Leblouba, S. Messaoudi; On the well-posedness and stability for a coupled nonlinear suspension bridge problem, Commun. Pure Appl. Anal., 22 (2023), 2716-2743.
J. Y. Park, J. R. Kang; Global attractors for the suspension bridge equations, Quart. Appl. Math., 69 (2011), 465-475.
C. Y. Sun, D. M. Cao, J. Q. Duan; Uniform attractors for nonautonomous wave equations with nonlinear damping, SIAM J. Appl. Dyn. Syst., 6 (2007), 293-318.
S. P.Wang, Q. Z. Ma; Uniform attractors for the non-autonomous suspension bridge equation with time delay, J. Inequal. Appl., 180 (2019), 1-17.
S. P. Wang, Q. Z. Ma; Existence of pullback attractors for the non-autonomous suspension bridge equation with time delay. Discrete Contin. Dyn. Syst. B., 25 (2020), 1299-1316.
S. P. Wang, Q. Z. Ma, X. K. Shao; Dynamics of suspension bridge equation with delay, J. Dyn. Diff. Equ., 35 (2023), 3563-3588.
C. K. Zhong, Q. Z. Ma, C. Y. Sun; Existence of strong solutions and global attractors for the suspension bridge equations, Nonlinear Anal., 67 (2007), 442-454.
Downloads
Published
License
Copyright (c) 2024 Lulu Wang, Qiaozhen Ma
This work is licensed under a Creative Commons Attribution 4.0 International License.
