Global and pullback attractors of set-valued skew product flows

We investigate the asymptotic behaviour of a general set-valued skew product flow (SVSPF), that is, a set-valued cocycle mapping (coming from a non-autonomous differential equation or inclusion) driven by another, autonomous, system. Absorptivity conditions which ensure the existence of several type...

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Bibliographic Details
Published in:Annali di matematica pura ed applicata 2006-01, Vol.185 (S5), p.S23-S45
Main Authors: Caraballo, T., Kloeden, P.E., Marín-Rubio, P.
Format: Article
Language:English
Subjects:
Absorptivity
Asymptotic properties
Attractors (mathematics)
Differential equations
Mapping
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Summary:We investigate the asymptotic behaviour of a general set-valued skew product flow (SVSPF), that is, a set-valued cocycle mapping (coming from a non-autonomous differential equation or inclusion) driven by another, autonomous, system. Absorptivity conditions which ensure the existence of several types of attractors for such set-valued systems are established. The topological properties of and relations between these attractors, in forward and pullback senses and their strong and weak versions are analyzed. Several illustrative examples are also provided.
ISSN:0373-3114
1618-1891
DOI:10.1007/s10231-004-0135-3