Attractors for Second Order Lattice Dynamical Systems

Zhou, Sizhong

doi:10.1006/jdeq.2001.4032

Cited by 95 publications

(64 citation statements)

References 7 publications

(14 reference statements)

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“…Proof By using Lemmas 1 and 2, the proof of this lemma will be similar to that of Lemma 3.2 of [26].…”

Section: Lemma 3 the Solution Semigroup {S(t)} T≥0 Generated By The Smentioning

confidence: 98%

Long-Time Behavior for Second Order Lattice Dynamical Systems

Abdallah

2008

Acta Appl Math

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Many researchers examined the existence of global attractors for various types of first and second order lattice dynamical systems. Here we prove the existence of a global attractor for a new type of second order lattice dynamical systems in the Hilbert space l 2 × l 2 . For specific choices of the linear operators this system can be regraded as a spatial discretization of a continuous damped nonlinear Boussinesq equation on R m , m ≥ 1.

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“…Proof By using Lemmas 1 and 2, the proof of this lemma will be similar to that of Lemma 3.2 of [26].…”

Section: Lemma 3 the Solution Semigroup {S(t)} T≥0 Generated By The Smentioning

confidence: 98%

Long-Time Behavior for Second Order Lattice Dynamical Systems

Abdallah

2008

Acta Appl Math

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“…"Tail ends" estimate method is usually used to get asymptotic compactness of autonomous infinite-dimensional lattice, and by this the existence of global compact attractor is obtained; see [15][16][17] . Authors in 18, 19 also prove that the uniform smallness of solutions of autonomous infinite lattice systems for large space and time variables is sufficient and necessary conditions for asymptotic compactness of it.…”

Section: Advances In Difference Equationsmentioning

confidence: 99%

Uniform Attractor for the Partly Dissipative Nonautonomous Lattice Systems

Lü²

2009

Advances in Difference Equations

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The existence of uniform attractor in l 2 × l 2 is proved for the partly dissipative nonautonomous lattice systems with a new class of external terms belonging to L 2 loc R, l 2 , which are locally asymptotic smallness and translation bounded but not translation compact in L 2 loc R, l 2 . It is also showed that the family of processes corresponding to nonautonomous lattice systems with external terms belonging to weak topological space possesses uniform attractor, which is identified with the original one. The upper semicontinuity of uniform attractor is also studied.

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“…In recent years, global attractors, uniform attractors, pullback attractors (or kernel sections), and random attractor for autonomous, nonautonomous, and stochastic LDSs have been studied; see [3][4][5][6][7][8][9][10][11][12]. However, these attractors sometimes attract orbits at a relatively slow speed, so that it might take an unexpected long time to be reached.…”

Section: Introductionmentioning

confidence: 99%

Pullback Exponential Attractor for Second Order Nonautonomous Lattice System

Zhou

Chen

Wang

2014

Discrete Dynamics in Nature and Society

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We first present some sufficient conditions for the existence of a pullback exponential attractor for continuous process on the product space of the weighted spaces of infinite sequences. Then we prove the existence and continuity of a pullback exponential attractor for second order lattice system with time-dependent coupled coefficients in the weighted space of infinite sequences. Moreover, we obtain the upper bound of fractal dimension and attracting rate for the attractor.

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Attractors for Second Order Lattice Dynamical Systems

Abstract: We consider the existence and the approximation of the global attractor for second order damped lattice dynamical systems.

Cited by 95 publications

References 7 publications

Long-Time Behavior for Second Order Lattice Dynamical Systems

Long-Time Behavior for Second Order Lattice Dynamical Systems

Uniform Attractor for the Partly Dissipative Nonautonomous Lattice Systems

Pullback Exponential Attractor for Second Order Nonautonomous Lattice System

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