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Existence of strong solutions and global attractors for the suspension bridge equations. (English) Zbl 1125.34019
The authors treat a nonlinear ordinary second-order differential equation by establishing some a priori bounds and then proving the convergence of the Faedo-Galerkin approximation method. Unfortunately, the equation does not describe the deflection of a suspension bridge, whose equation is completely different. In addition, the language is poor and full of mistakes, and the references ignore the huge, classical, literature of the problem.

MSC:
34B45Boundary value problems for ODE on graphs and networks
34C60Qualitative investigation and simulation of models (ODE)
35B41Attractors (PDE)
74H45Vibrations (dynamical problems in solid mechanics)
34D05Asymptotic stability of ODE
35Q72Other PDE from mechanics (MSC2000)
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References:
[1] Lazer, A. C.; Mckenna, P. J.: Large-amplitude periodic oscillations in suspension bridges: some new connections with nonlinear analysis. SIAM rev. 32, No. 4, 537-578 (1990) · Zbl 0725.73057
[2] Humphreys, L. D.: Numerical mountain pass solutions of a suspension Bridge equation. Nonlinear anal.(TMA) 28, No. 11, 1811-1826 (1997) · Zbl 0877.35126
[3] Lazer, A. C.; Mckenna, P. J.: Large scale oscillatory behavior in loaded asymmetric systems. Nonlinear. anal. I. H.P. 4, 243-274 (1987) · Zbl 0633.34037
[4] Mckenna, P. J.; Walter, W.: Nonlinear oscillation in a suspension Bridge. Non. anal. 39, 731-743 (2000)
[5] Choi, Q. H.; Jung, T.: A nonlinear suspension Bridge equation with nonconstant load. Nonlinear. anal. 35, 649-668 (1999) · Zbl 0934.74031
[6] Y. An, On the Suspension Bridge Equations and the Relevant Problems, Doctoral Thesis, 2001
[7] Ma, Q. F.; Wang, S. H.; Zhong, C. K.: Necessary and sufficient conditions for the existence of global attractor for semigroup and application. Indiana univ. Math. J. 51, No. 6, 1541-1559 (2002) · Zbl 1028.37047
[8] Temam, R.: Infinite dimensional dynamical system in mechanics and physics. (1997) · Zbl 0871.35001
[9] Ma, Q. Z.; Zhong, C. K.: Existence of strong global attractors for hyperbolic equation with linear memory. Appl. math. Comput. 157, 745-758 (2004) · Zbl 1068.45018
[10] Ball, J. M.: Initial--boundary value problems for an extensible beam. J. math. Anal. appl. 42, 61-90 (1973) · Zbl 0254.73042
[11] Ma, Q. Z.; Zhong, C. K.: Existence of global attractors for the suspension Bridge equations. J. sichuan univ. 43, No. 2 (2006) · Zbl 1111.35089
[12] Ma, Q. Z.; Zhong, C. K.: Global attractors of strong solutions for nonclassical diffusion equation. J. Lanzhou univ. 40, No. 5, 7-9 (2004) · Zbl 1090.35145
[13] Zhong, C. K.; Yang, M. H.; Sun, C. Y.: The existence of global attractors for the norm-to-weak continuous semigroup and application to the nonlinear reaction--diffusion equations. J. differential equations. 223, No. 2, 367-399 (2006) · Zbl 1101.35022
[14] Hale, J. K.: Asymptotic behavior of dissipative systems. (1988) · Zbl 0642.58013