CPAA
Asymptotic behavior of the Klein-Gordon-Schrödinger lattice dynamical systems
Ahmed Y. Abdallah
Communications on Pure & Applied Analysis 2006, 5(1): 55-69 doi: 10.3934/cpaa.2006.5.55
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.
keywords: global attractor upper semicontinuity. Lattice dynamical system absorbing set Klein-Gordon-Schrödinger equation
CPAA
Exponential attractors for second order lattice dynamical systems
Ahmed Y. Abdallah
Communications on Pure & Applied Analysis 2009, 8(3): 803-813 doi: 10.3934/cpaa.2009.8.803
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 $l^2\times l^2$.
keywords: squeezing property Lattice dynamical system exponential attractor.
DCDS-B
Upper semicontinuity of the attractor for a second order lattice dynamical system
Ahmed Y. Abdallah
Discrete & Continuous Dynamical Systems - B 2005, 5(4): 899-916 doi: 10.3934/dcdsb.2005.5.899
We study the existence and the upper semicontinuity of the global attractor for a second order lattice dynamical system.
keywords: Lattice dynamical system absorbing set upper semicontinuity. global attractor

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