Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

Global attractors for the suspension bridge equations with nonlinear damping


Authors: Jong-Yeoul Park and Jum-Ran Kang
Journal: Quart. Appl. Math. 69 (2011), 465-475
MSC (2010): Primary 35B40, 35B41, 35Q35
DOI: https://doi.org/10.1090/S0033-569X-2011-01259-1
Published electronically: April 25, 2011
MathSciNet review: 2850741
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we prove the existence of a global attractor for the suspension bridge equations with nonlinear damping.


References [Enhancements On Off] (What's this?)

  • 1. N. U. Ahmed and H. Harbi, Mathematical analysis of dynamic models of suspension bridges, SIAM J. Appl. Math. 58 (1998) 853-874. MR 1616611 (99d:73050)
  • 2. Y. An, On the suspension bridge equations and the relevant problems, Doctoral Thesis, 2001.
  • 3. I. Chueshov and I. Lasiecka, Attractors for second-order evolution equations with nonlinear damping, J. Dynam. Differential Equations 16 (2004) 469-512. MR 2105786 (2005g:37149)
  • 4. I. Chueshov and I. Lasiecka, Long-time dynamics of von Karman semi-flows with non-linear boundary/interior damping, J. Differential Equations 233 (2007) 42-86. MR 2290271 (2008a:37091)
  • 5. A. Kh. Khanmamedov, Global attractors for von Karman equations with nonlinear interior damping, J. Math. Anal. Appl. 318 (2006) 92-101. MR 2210874 (2007b:37198)
  • 6. A. Kh. Khanmamedov, Finite dimensionality of the global attractors for von Karman equations with nonlinear interior dissipation, Nonlinear Anal. 66 (2007) 204-213. MR 2271647 (2007f:35209)
  • 7. A. Kh. Khanmamedov, Global attractors for wave equations with nonlinear interior damping and critical exponents, J. Differential Equations 230 (2006) 702-719. MR 2269940 (2007i:37150)
  • 8. A. Kh. Khanmamedov, Global attractors for the plate equation with a localized damping and a critical exponent in an unbounded domain, J. Differential Equations 225 (2006)528-548. MR 2225799 (2007a:37100)
  • 9. 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. MR 1084570 (92g:73059)
  • 10. 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. MR 2142424 (2006b:37167)
  • 11. Q.Z. Ma and C.K. Zhong, Existence of global attractors for the suspension bridge equations, J. Sichuan Univ. 43 (2) (2006). MR 2226668
  • 12. P. J. McKenna and W. Walter, Nonlinear oscillation in a suspension bridge, Nonlinear Anal. 39 (2000) 731-743.
  • 13. J.Y. Park and J.R. Kang, Pullback $ {\mathcal D}$-attractors for non-autonomous suspension bridge equations, Nonlinear Anal. 71 (2009) 4618-4623. MR 2548694 (2010i:35258)
  • 14. R. Temam, Infinite-dimensional Dynamical Systems in Mechanics and Physics, Springer-Verlag, 1997. MR 1441312 (98b:58056)
  • 15. L. Yang and C.K. Zhong, Global attractor for plate equation with nonlinear damping, Nonlinear Anal. 69 (2008) 3802-3810. MR 2463335 (2009k:35211)
  • 16. C.K. Zhong, Q.Z. Ma, and C.Y. Sun, Existence of strong solutions and global attractors for the suspension bridge equations, Nonlinear Analysis 67 (2007) 442-454. MR 2317179 (2008h:35250)

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC (2010): 35B40, 35B41, 35Q35

Retrieve articles in all journals with MSC (2010): 35B40, 35B41, 35Q35


Additional Information

Jong-Yeoul Park
Affiliation: Department of Mathematics, Pusan National University, Busan 609-735, Korea
Email: jyepark@pusan.ac.kr

Jum-Ran Kang
Affiliation: Department of Mathematics, Dong-A University, Busan 604-714, Korea
Email: jrkang@donga.ac.kr

DOI: https://doi.org/10.1090/S0033-569X-2011-01259-1
Keywords: Suspension bridge equations, Global attractor, Nonlinear damping
Received by editor(s): November 25, 2009
Published electronically: April 25, 2011
Additional Notes: The second author is the corresponding author
Article copyright: © Copyright 2011 Brown University
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society