THE EXISTENCE OF GLOBAL ATTRACTORS FOR SUSPENSION BRIDGE EQUATIONS

Year 2019, Volume: 37 Issue: 4, 1348 - 1366, 01.12.2019

Mohamed Ferhat Fatima Zohra Mahdı Ali Hakem

Abstract

The aim of this paper is to establish a well-posedness result and the existence of finite- dimensional global attractors for a model of a coupled suspension bridge as well as the regularity of global attractor is achieved. This result generalizes the previous result in [6].

Keywords

Suspension bridge, global attractors, bounded absorbing set.

References

• [1] I. Chueshov, I. Lasiecka, Von Karman Evolution Equations: Well-Posedness and Long-Time Dynamics, Springer Monographs in Mathematics, Springer, New York, 2010.
• [2] C. M. Dafermos, Asymptotic stability in viscoelasticity, Arch. Ration. Mech. Anal. (1970)37, pp. 204-229.
• [3] F. Gazzola, Mathematical Models for Suspension Bridges Nonlinear Structural Instability, Springer international publishing Switzerland 2015.
• [4] J.R. Kang, Asymptotic behavior of the thermoelastic suspension bridge equation with linear memory, Bound Value Probl (2016) 206. 1-18.
• [5] A.C. Lazer, P.J. McKenna, Large-amplitude periodic oscillations in suspension bridges: Some new connections with nonlinear analysis, SIAM Rev. 32 1990; 4: 537-578.
• [6] S. Liu, Q. Ma, Global attractors and regularity for the extensible suspension bridge equations with past history, Korean J. Math. 24 (2016), No. 3, pp. 375-395.
• [7] Q. Ma, B. Wang, Existence of pullback attractors for the coupled suspension bridge equations, Electronic Journal of Differential Equations, Vol. 2011 (2011), No. 16, pp. 1-10.
• [8] S. A. Messaoudi, A. Bonfoh, S. E. Mukiawa, C. D. Enyid, The global attractor for a suspension bridge with memory and partially hinged boundary conditions, Z. Angew. Math. Mech 97(2)(2017) 1-14.
• [9] J.Y. Park, J.R. Kang, Pullback D-attractors for non-autonomous suspension bridge equations, Nonlinear Anal.71(2009), pp. 4618-4623.
• [10] J.Y. Park, J.R. Kang, Global attractors for the suspension bridge equations with non- linear damp ing, Quart.Appl.Math.69(2011), pp. 465-475.
• [11] R. Temam, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Appl. Math. Sci, Vol. 68, Springer-Verlag, New York, 1988.
• [12] M. Como, S. Del Ferraro, A. Grimaldi, A parametric analysis of the flutter instability for long span suspension bridges, Wind and Structures 8, 1-12 (2005).
• [13] Feng.B, Pelicer.M.L, Andrade. D Long-time behavior of a semilinear wave equation with memory, Boundary Value Problems 37(2016).
• [14] Feng. B Long-time dynamics of a plate equation with memory and time delay, Bull. Braz. Math. Society, 49 1-24(2018).
• [15] Monica.C, Pelin.G.G Existence of smooth global attractors for nonlinear viscoelastic equations with memory, J.Evol.Equa 15 533-558(2015).