- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 869621, 6 pages
Exponential Attractor for Lattice System of Nonlinear Boussinesq Equation
Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China
Received 14 July 2013; Accepted 13 August 2013
Academic Editor: Zhan Zhou
Copyright © 2013 Min Zhao and Shengfan Zhou. 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.
- H. Chate and M. Courbage, “Lattice systems,” Physica D, vol. 103, no. 1–4, pp. 1–612, 1997.
- S. N. Chow, Lattice Dynamical Systems, in Dynamical System, vol. 1822 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 2003.
- A. Y. Abdallah, “Global attractor for the lattice dynamical system of a nonlinear Boussinesq equation,” Abstract and Applied Analysis, vol. 2005, no. 6, pp. 655–671, 2005.
- A. Y. Abdallah, “Long-time behavior for second order lattice dynamical systems,” Acta Applicandae Mathematicae, vol. 106, no. 1, pp. 47–59, 2009.
- P. W. Bates, K. Lu, and B. Wang, “Attractors for lattice dynamical systems,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 11, no. 1, pp. 143–153, 2001.
- H. Li and S. Zhou, “Structure of the global attractor for a second order strongly damped lattice system,” Journal of Mathematical Analysis and Applications, vol. 330, no. 2, pp. 1426–1446, 2007.
- J. C. Oliveira, J. M. Pereira, and G. Perla Menzala, “Attractors for second order periodic lattices with nonlinear damping,” Journal of Difference Equations and Applications, vol. 14, no. 9, pp. 899–921, 2008.
- B. Wang, “Dynamics of systems on infinite lattices,” Journal of Differential Equations, vol. 221, no. 1, pp. 224–245, 2006.
- C. Zhao and S. Zhou, “Upper semicontinuity of attractors for lattice systems under singular perturbations,” Nonlinear Analysis, Theory, Methods and Applications, vol. 72, no. 5, pp. 2149–2158, 2010.
- S. Zhou, “Attractors for second order lattice dynamical systems,” Journal of Differential Equations, vol. 179, no. 2, pp. 605–624, 2002.
- S. Zhou, “Attractors and approximations for lattice dynamical systems,” Journal of Differential Equations, vol. 200, no. 2, pp. 342–368, 2004.
- X. Fan and H. Yang, “Exponential attractor and its fractal dimension for a second order lattice dynamical system,” Journal of Mathematical Analysis and Applications, vol. 367, no. 2, pp. 350–359, 2010.
- X. Han, “Exponential attractors for lattice dynamical systems in weighted spaces,” Discrete and Continuous Dynamical Systems, vol. 31, no. 2, pp. 445–467, 2011.
- A. Y. Abdallah, “Exponential attractors for second order lattice dynamical systems,” Communications on Pure and Applied Analysis, vol. 8, no. 3, pp. 803–813, 2009.
- S. Zhou and X. Han, “Uniform exponential attractors for non-autonomous KGS and Zakharov lattice systems with quasiperiodic external forces,” Nonlinear Analysis: Theory, Methods & Applications, vol. 78, pp. 141–155, 2013.