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The relationship between pullback, forward and global attractors of nonautonomous dynamical systems. (English) Zbl 1054.34087
The authors study and compare various types of attractors for nonautonomous dynamical systems involving a cocycle state space driven by an autonomous dynamical system on a compact state space. In particular, they give conditions for a uniform pullback attractor to form a global attractor of the associated autonomous skew-product semi-dynamical system. They generalize Zubov’s theorem on the characterization of the asymptotic stability of a compact set with respect to an α-condensing semi-dynamical system. The results are illustrated by several examples – in particular by a nonautonomous Navier-Stokes equation – that are generated by differential equations on a Banach space with a uniform dissipative structur induced by a monotone operator.
MSC:
34D45Attractors
35B41Attractors (PDE)
34D20Stability of ODE
34D40Ultimate boundedness (MSC2000)
34G20Nonlinear ODE in abstract spaces
35B35Stability of solutions of PDE
35B40Asymptotic behavior of solutions of PDE
35Q30Stokes and Navier-Stokes equations
37C70Attractors and repellers, topological structure
37C75Stability theory