• Previous Article
    Equivalence of invariant measures and stationary statistical solutions for the autonomous globally modified Navier-Stokes equations
  • CPAA Home
  • This Issue
  • Next Article
    Global well-posedness and non-linear stability of periodic traveling waves for a Schrödinger-Benjamin-Ono system
May  2009, 8(3): 803-813. doi: 10.3934/cpaa.2009.8.803

Exponential attractors for second order lattice dynamical systems

1. 

Department of Mathematics, University of Jordan, Amman 11942, Jordan

Received  May 2008 Revised  November 2008 Published  February 2009

In [3], we introduced for the first time the study of exponential attractors for lattice dynamical systems, where a first order system has been investigated. Here we shall examine the existence of an exponential attractor for the solution semigroup of a second order lattice dynamical system acting on a closed bounded positively invariant set in the Hilbert space $l^2\times l^2$.
Citation: Ahmed Y. Abdallah. Exponential attractors for second order lattice dynamical systems. Communications on Pure & Applied Analysis, 2009, 8 (3) : 803-813. doi: 10.3934/cpaa.2009.8.803
[1]

Ahmed Y. Abdallah. Upper semicontinuity of the attractor for a second order lattice dynamical system. Discrete & Continuous Dynamical Systems - B, 2005, 5 (4) : 899-916. doi: 10.3934/dcdsb.2005.5.899

[2]

Xiaoying Han. Exponential attractors for lattice dynamical systems in weighted spaces. Discrete & Continuous Dynamical Systems - A, 2011, 31 (2) : 445-467. doi: 10.3934/dcds.2011.31.445

[3]

Fang-Di Dong, Wan-Tong Li, Li Zhang. Entire solutions in a two-dimensional nonlocal lattice dynamical system. Communications on Pure & Applied Analysis, 2018, 17 (6) : 2517-2545. doi: 10.3934/cpaa.2018120

[4]

Shi-Liang Wu, Cheng-Hsiung Hsu. Entire solutions with merging fronts to a bistable periodic lattice dynamical system. Discrete & Continuous Dynamical Systems - A, 2016, 36 (4) : 2329-2346. doi: 10.3934/dcds.2016.36.2329

[5]

Jong-Shenq Guo, Ying-Chih Lin. Traveling wave solution for a lattice dynamical system with convolution type nonlinearity. Discrete & Continuous Dynamical Systems - A, 2012, 32 (1) : 101-124. doi: 10.3934/dcds.2012.32.101

[6]

Jong-Shenq Guo, Chang-Hong Wu. Front propagation for a two-dimensional periodic monostable lattice dynamical system. Discrete & Continuous Dynamical Systems - A, 2010, 26 (1) : 197-223. doi: 10.3934/dcds.2010.26.197

[7]

Chin-Chin Wu. Monotonicity and uniqueness of wave profiles for a three components lattice dynamical system. Discrete & Continuous Dynamical Systems - A, 2017, 37 (5) : 2813-2827. doi: 10.3934/dcds.2017121

[8]

Zhaoquan Xu, Jiying Ma. Monotonicity, asymptotics and uniqueness of travelling wave solution of a non-local delayed lattice dynamical system. Discrete & Continuous Dynamical Systems - A, 2015, 35 (10) : 5107-5131. doi: 10.3934/dcds.2015.35.5107

[9]

W. Patrick Hooper. An infinite surface with the lattice property Ⅱ: Dynamics of pseudo-Anosovs. Journal of Modern Dynamics, 2019, 14: 243-276. doi: 10.3934/jmd.2019009

[10]

Tomás Caraballo, Francisco Morillas, José Valero. Asymptotic behaviour of a logistic lattice system. Discrete & Continuous Dynamical Systems - A, 2014, 34 (10) : 4019-4037. doi: 10.3934/dcds.2014.34.4019

[11]

Dalibor Pražák. Exponential attractor for the delayed logistic equation with a nonlinear diffusion. Conference Publications, 2003, 2003 (Special) : 717-726. doi: 10.3934/proc.2003.2003.717

[12]

Messoud Efendiev, Anna Zhigun. On an exponential attractor for a class of PDEs with degenerate diffusion and chemotaxis. Discrete & Continuous Dynamical Systems - A, 2018, 38 (2) : 651-673. doi: 10.3934/dcds.2018028

[13]

Xinyuan Liao, Caidi Zhao, Shengfan Zhou. Compact uniform attractors for dissipative non-autonomous lattice dynamical systems. Communications on Pure & Applied Analysis, 2007, 6 (4) : 1087-1111. doi: 10.3934/cpaa.2007.6.1087

[14]

Caidi Zhao, Shengfan Zhou. Compact uniform attractors for dissipative lattice dynamical systems with delays. Discrete & Continuous Dynamical Systems - A, 2008, 21 (2) : 643-663. doi: 10.3934/dcds.2008.21.643

[15]

Ahmed Y. Abdallah. Asymptotic behavior of the Klein-Gordon-Schrödinger lattice dynamical systems. Communications on Pure & Applied Analysis, 2006, 5 (1) : 55-69. doi: 10.3934/cpaa.2006.5.55

[16]

Tomás Caraballo, Francisco Morillas, José Valero. On differential equations with delay in Banach spaces and attractors for retarded lattice dynamical systems. Discrete & Continuous Dynamical Systems - A, 2014, 34 (1) : 51-77. doi: 10.3934/dcds.2014.34.51

[17]

Anhui Gu. Asymptotic behavior of random lattice dynamical systems and their Wong-Zakai approximations. Discrete & Continuous Dynamical Systems - B, 2017, 22 (11) : 1-31. doi: 10.3934/dcdsb.2019104

[18]

Wenlei Li, Shaoyun Shi. Weak-Painlevé property and integrability of general dynamical systems. Discrete & Continuous Dynamical Systems - A, 2014, 34 (9) : 3667-3681. doi: 10.3934/dcds.2014.34.3667

[19]

Manfred G. Madritsch, Izabela Petrykiewicz. Non-normal numbers in dynamical systems fulfilling the specification property. Discrete & Continuous Dynamical Systems - A, 2014, 34 (11) : 4751-4764. doi: 10.3934/dcds.2014.34.4751

[20]

Adina Luminiţa Sasu, Bogdan Sasu. Discrete admissibility and exponential trichotomy of dynamical systems. Discrete & Continuous Dynamical Systems - A, 2014, 34 (7) : 2929-2962. doi: 10.3934/dcds.2014.34.2929

2018 Impact Factor: 0.925

Metrics

  • PDF downloads (7)
  • HTML views (0)
  • Cited by (14)

Other articles
by authors

[Back to Top]