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Attractors for lattice dynamical systems. (English) Zbl 1091.37515

Summary: We study the asymptotic behavior of solutions for lattice dynamical systems. We first prove asymptotic compactness and then establish the existence of global attractors. The upper semicontinuity of the global attractor is also obtained when the lattice differential equations are approached by finite-dimensional systems.

MSC:

37L60 Lattice dynamics and infinite-dimensional dissipative dynamical systems
37L30 Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems
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