IMCS/Publications/BASM/Issues/BASM n.2 (27), 1998/

Global attractors of infinite-dimensional nonautonomous dynamical systems. II. (English)

Authors: Cheban D. N.


The article is devoted to the infinite-dimensional abstract nonautonomous dynamical systems which admit the compact global attractor. It is shown that nonautonomous dynamical system which has the bounded absorbing (weakly absorbing) set also has a compact global attractor if its operators of translation along the trajectories are compact (asymptotically compact; satisfy the condition of Ladyzhenskaya). These results are made more precise and strengthened for the nonautonomous dynamical systems with minimal basis. The conditions of existence of the compact global attractor for the skew-product dynamical systems (cocycles) are presented. The necessary and sufficient conditions of the existence of compact global attractor are given in terms of Lyapunov functions. The applications of obtained results for the different classes of the evolutionary equations are given.

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