RO  EN
IMI/Publicaţii/BASM/Ediţii/BASM n.3 (25), 1997/

Global attractors of infinite-dimensional nonautonomous dynamical systems. I. (Russian)

Authors: Cheban D. N.

Abstract

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; satisfies the condition of Ladyjenskaja). This results are precised 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 Lypunov functions. The applications of obtained results for the different classes of the evolutionary equations are given.

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