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Asymptotic behavior of non-autonomous lattice systems. (English) Zbl 1112.37076
Summary: The asymptotic behavior of nonautonomous infinite-dimensional lattice systems is studied. It is shown that the nonautonomous lattice reaction-diffusion system has a compact uniform attractor. The uniform asymptotic compactness of the system is established by showing that the tails of the solutions are uniformly small when time goes to infinity. The upper semicontinuity of uniform attractors is also obtained when the infinite-dimensional reaction-diffusion system is approached by a family of finite-dimensional systems.

MSC:
37L60 Lattice dynamics and infinite-dimensional dissipative dynamical systems
35K57 Reaction-diffusion equations
35B41 Attractors
35B40 Asymptotic behavior of solutions to PDEs
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