Attractors for Second Order Lattice Dynamical Systems
TLDR
In this article, the existence and approximation of the global attractor for second order damped lattice dynamical systems was studied. But the approximation was not considered for the case where the lattice lattice is not convex.About:
This article is published in Journal of Differential Equations.The article was published on 2002-03-01 and is currently open access. It has received 84 citations till now. The article focuses on the topics: Attractor & Random dynamical system.read more
Citations
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Journal ArticleDOI
Infinite-Dimensional Dynamical Systems in Mechanics and Physics (Roger Temam)
TL;DR: 5. M. Green, J. Schwarz, and E. Witten, Superstring theory, and An interpretation of classical Yang-Mills theory, Cambridge Univ.
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Dynamics of systems on infinite lattices
TL;DR: In this article, a necessary and sufficient condition for asymptotic compactness of lattice dynamical systems is introduced, and it is shown that a lattice system has a global attractor if and only if it has a bounded absorbing set and is asmptotically null.
Journal ArticleDOI
Random attractors for stochastic lattice dynamical systems in weighted spaces
TL;DR: In this article, the existence of global compact random attractors in weighted space l ρ 2 for stochastic lattice dynamical systems with random coupled coefficients and multiplicative/additive white noises was shown.
Journal ArticleDOI
Attractors and approximations for lattice dynamical systems
TL;DR: In this article, a sufficient condition for the existence of a global attractor for general lattice dynamical systems is presented, and the existence and approximation of an attractor is investigated for second-order and first-order lattice systems.
References
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Book
Partial Differential Equations
TL;DR: In this paper, the authors present a theory for linear PDEs: Sobolev spaces Second-order elliptic equations Linear evolution equations, Hamilton-Jacobi equations and systems of conservation laws.
Book
Asymptotic Behavior of Dissipative Systems
TL;DR: In this article, the authors consider a continuous dynamical system with a global attractor and describe the properties of the flow on the attractor asymptotically smooth and Morse-Smale maps.
Journal ArticleDOI
Infinite-Dimensional Dynamical Systems in Mechanics and Physics (Roger Temam)
TL;DR: 5. M. Green, J. Schwarz, and E. Witten, Superstring theory, and An interpretation of classical Yang-Mills theory, Cambridge Univ.
Journal ArticleDOI
Attractors for lattice dynamical systems
TL;DR: This work first proves asymptotic compactness and then establishes the existence of global attractors and the upper semicontinuity of the global attractor is also obtained when the lattice differential equations are approached by finite-dimensional systems.
Journal Article
Attractors for damped nonlinear hyperbolic equations
TL;DR: In this paper, the authors consider des equations hyperboliques non lineaires amorties telles que l'equation sinus-Gordon ou l'Equation d'onde non lineaire de la mecanique quantique.