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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 359310, 9 pages
http://dx.doi.org/10.1155/2013/359310
Research Article

On the Dynamics of Abstract Retarded Evolution Equations

1Department of Mathematics, School of Science, Tianjin University, Tianjin 300072, China
2School of Electrical Engineering and Automation, Tianjin University, Tianjin 300072, China
3School of Mathematics, Lanzhou City University, Lanzhou 730020, China

Received 20 July 2013; Accepted 30 August 2013

Academic Editor: Carlo Bianca

Copyright © 2013 Desheng Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. T. Caraballo, P. Marín-Rubio, and J. Valero, “Autonomous and non-autonomous attractors for differential equations with delays,” Journal of Differential Equations, vol. 208, no. 1, pp. 9–41, 2005. View at Publisher · View at Google Scholar · View at Scopus
  2. T. Caraballo, M. J. Garrido-Atienza, B. Schmalfuss, and J. Valero, “Non-autonomous and random attractors for delay random semilinear equations without uniqueness,” Discrete and Continuous Dynamical Systems, vol. 21, no. 2, pp. 415–443, 2008. View at Scopus
  3. T. Caraballo and J. Real, “Attractors for 2D-Navier-Stokes models with delays,” Journal of Differential Equations, vol. 205, no. 2, pp. 271–297, 2004. View at Publisher · View at Google Scholar · View at Scopus
  4. J. Li and J. Huang, “Uniform attractors for non-autonomous parabolic equations with delays,” Nonlinear Analysis, Theory, Methods and Applications, vol. 71, no. 5-6, pp. 2194–2209, 2009. View at Publisher · View at Google Scholar · View at Scopus
  5. M. A. Ragusa, “Cauchy-Dirichlet problem associated to divergence form parabolic equations,” Communications in Contemporary Mathematics, vol. 6, no. 3, pp. 377–393, 2004. View at Publisher · View at Google Scholar · View at Scopus
  6. A. V. Rezounenko, “Partial differential equations with discrete and distributed state-dependent delays,” Journal of Mathematical Analysis and Applications, vol. 326, no. 2, pp. 1031–1045, 2007. View at Publisher · View at Google Scholar · View at Scopus
  7. A. V. Rezounenko, “A condition on delay for differential equations with discrete state-dependent delay,” Journal of Mathematical Analysis and Applications, vol. 385, no. 1, pp. 506–516, 2012. View at Publisher · View at Google Scholar · View at Scopus
  8. J. W.-H. So and J. H. Wu, “Topological dimensions of global attractors for semilinear PDEs with delays,” Bulletin of the Australian Mathematical Society, vol. 43, no. 3, pp. 407–422, 1991. View at Publisher · View at Google Scholar
  9. G. R. Sell and Y. You, “Dynamics of evolutionary equations,” in Applied Mathematical Sciences, vol. 143, Springer, New York, NY, USA, 2002.
  10. Y. X. Li, “Existence and asymptotic stability of periodic solution for evolution equations with delays,” Journal of Functional Analysis, vol. 261, no. 5, pp. 1309–1324, 2011. View at Publisher · View at Google Scholar · View at Scopus
  11. V. P. Bongolan-Walsh, D. Cheban, and J. Duan, “Recurrent motions in the nonautonomous Navier-Stokes system,” Discrete and Continuous Dynamical Systems B, vol. 3, no. 2, pp. 255–262, 2003. View at Scopus
  12. G. R. Sell, “Topological dynamics and ordinary differential equations,” in Van Nostrand Reinhold Mathematical Studies, vol. 33, Van Nostrand Reinhold, London, UK, 1971.
  13. D. N. Cheban, P. E. Kloeden, and B. Schmalfuss, “The relationship between pullback, for- wards and global attractors of nonautonomous dynamical systems,” Nonlinear Dynamics and Systems Theory, vol. 2, pp. 125–144, 2002.
  14. V. V. Chepyzhov and M. I. Vishik, Attractors for Equations of Mathematical Physics, vol. 49, American Mathematical Society, Providence, RI, USA, 2002.
  15. H. Song and H. Wu, “Pullback attractors of nonautonomous reaction-diffusion equations,” Journal of Mathematical Analysis and Applications, vol. 325, no. 2, pp. 1200–1215, 2007. View at Publisher · View at Google Scholar · View at Scopus
  16. G. D. Birkhoff, “Dynamical systems,” in American Mathematical Society Colloquium, vol. 9, American Mathematical Society, Providence, RI, USA, 1927.