• Previous Article
    On the uniqueness of ground state solutions of a semilinear equation containing a weighted Laplacian
  • CPAA Home
  • This Issue
  • Next Article
    Existence and nonexistence results for a class of parabolic equations with mixed boundary conditions
March  2006, 5(1): 55-69. doi: 10.3934/cpaa.2006.5.55

Asymptotic behavior of the Klein-Gordon-Schrödinger lattice dynamical systems

1. 

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

Received  March 2005 Revised  November 2005 Published  December 2005

We investigate the existence of the global attractor and its upper semicontinuity for the lattice dynamical system of a Klein-Gordon-Schrödinger type equation in a suitable Hilbert space.
Citation: Ahmed Y. Abdallah. Asymptotic behavior of the Klein-Gordon-Schrödinger lattice dynamical systems. Communications on Pure and Applied Analysis, 2006, 5 (1) : 55-69. doi: 10.3934/cpaa.2006.5.55
[1]

Salah Missaoui, Ezzeddine Zahrouni. Regularity of the attractor for a coupled Klein-Gordon-Schrödinger system with cubic nonlinearities in $\mathbb{R}^2$. Communications on Pure and Applied Analysis, 2015, 14 (2) : 695-716. doi: 10.3934/cpaa.2015.14.695

[2]

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

[3]

Fábio Natali, Ademir Pastor. Orbital stability of periodic waves for the Klein-Gordon-Schrödinger system. Discrete and Continuous Dynamical Systems, 2011, 31 (1) : 221-238. doi: 10.3934/dcds.2011.31.221

[4]

Marilena N. Poulou, Nikolaos M. Stavrakakis. Finite dimensionality of a Klein-Gordon-Schrödinger type system. Discrete and Continuous Dynamical Systems - S, 2009, 2 (1) : 149-161. doi: 10.3934/dcdss.2009.2.149

[5]

Salah Missaoui. Regularity of the attractor for a coupled Klein-Gordon-Schrödinger system in $ \mathbb{R}^3 $ nonlinear KGS system. Communications on Pure and Applied Analysis, 2022, 21 (2) : 567-584. doi: 10.3934/cpaa.2021189

[6]

Ahmed Y. Abdallah, Taqwa M. Al-Khader, Heba N. Abu-Shaab. Attractors of the Klein-Gordon-Schrödinger lattice systems with almost periodic nonlinear part. Discrete and Continuous Dynamical Systems - B, 2022  doi: 10.3934/dcdsb.2022006

[7]

E. Compaan, N. Tzirakis. Low-regularity global well-posedness for the Klein-Gordon-Schrödinger system on $ \mathbb{R}^+ $. Discrete and Continuous Dynamical Systems, 2019, 39 (7) : 3867-3895. doi: 10.3934/dcds.2019156

[8]

Fábio Natali, Ademir Pastor. Stability properties of periodic standing waves for the Klein-Gordon-Schrödinger system. Communications on Pure and Applied Analysis, 2010, 9 (2) : 413-430. doi: 10.3934/cpaa.2010.9.413

[9]

Weizhu Bao, Chunmei Su. Uniform error estimates of a finite difference method for the Klein-Gordon-Schrödinger system in the nonrelativistic and massless limit regimes. Kinetic and Related Models, 2018, 11 (4) : 1037-1062. doi: 10.3934/krm.2018040

[10]

Pavlos Xanthopoulos, Georgios E. Zouraris. A linearly implicit finite difference method for a Klein-Gordon-Schrödinger system modeling electron-ion plasma waves. Discrete and Continuous Dynamical Systems - B, 2008, 10 (1) : 239-263. doi: 10.3934/dcdsb.2008.10.239

[11]

Caidi Zhao, Gang Xue, Grzegorz Łukaszewicz. Pullback attractors and invariant measures for discrete Klein-Gordon-Schrödinger equations. Discrete and Continuous Dynamical Systems - B, 2018, 23 (9) : 4021-4044. doi: 10.3934/dcdsb.2018122

[12]

Ji Shu. Random attractors for stochastic discrete Klein-Gordon-Schrödinger equations driven by fractional Brownian motions. Discrete and Continuous Dynamical Systems - B, 2017, 22 (4) : 1587-1599. doi: 10.3934/dcdsb.2017077

[13]

A. F. Almeida, M. M. Cavalcanti, J. P. Zanchetta. Exponential decay for the coupled Klein-Gordon-Schrödinger equations with locally distributed damping. Communications on Pure and Applied Analysis, 2018, 17 (5) : 2039-2061. doi: 10.3934/cpaa.2018097

[14]

Adriana Flores de Almeida, Marcelo Moreira Cavalcanti, Janaina Pedroso Zanchetta. Exponential stability for the coupled Klein-Gordon-Schrödinger equations with locally distributed damping. Evolution Equations and Control Theory, 2019, 8 (4) : 847-865. doi: 10.3934/eect.2019041

[15]

Zehan Lin, Chongbin Xu, Caidi Zhao, Chujin Li. Statistical solution and Kolmogorov entropy for the impulsive discrete Klein-Gordon-Schrödinger-type equations. Discrete and Continuous Dynamical Systems - B, 2022  doi: 10.3934/dcdsb.2022065

[16]

Marilena N. Poulou, Nikolaos M. Stavrakakis. Global attractor for a Klein-Gordon-Schrodinger type system. Conference Publications, 2007, 2007 (Special) : 844-854. doi: 10.3934/proc.2007.2007.844

[17]

Yang Han. On the cauchy problem for the coupled Klein Gordon Schrödinger system with rough data. Discrete and Continuous Dynamical Systems, 2005, 12 (2) : 233-242. doi: 10.3934/dcds.2005.12.233

[18]

María Astudillo, Marcelo M. Cavalcanti. On the upper semicontinuity of the global attractor for a porous medium type problem with large diffusion. Evolution Equations and Control Theory, 2017, 6 (1) : 1-13. doi: 10.3934/eect.2017001

[19]

Hartmut Pecher. Low regularity well-posedness for the 3D Klein - Gordon - Schrödinger system. Communications on Pure and Applied Analysis, 2012, 11 (3) : 1081-1096. doi: 10.3934/cpaa.2012.11.1081

[20]

Olivier Goubet, Marilena N. Poulou. Semi discrete weakly damped nonlinear Klein-Gordon Schrödinger system. Communications on Pure and Applied Analysis, 2014, 13 (4) : 1525-1539. doi: 10.3934/cpaa.2014.13.1525

2020 Impact Factor: 1.916

Metrics

  • PDF downloads (94)
  • HTML views (0)
  • Cited by (12)

Other articles
by authors

[Back to Top]