A minimal approach to the theory of global attractors

Vladimir V. Chepyzhov; Monica Conti; Vittorino Pata

doi:10.3934/dcds.2012.32.2079

Article Contents

2012, Volume 32, Issue 6: 2079-2088. Doi: 10.3934/dcds.2012.32.2079

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A minimal approach to the theory of global attractors

1.
Institute for Information Transmission Problems, Russian Academy of Sciences, Bolshoy Karetniy 19, Moscow 101447
2.
Dipartimento di Matematica “Francesco Brioschi”, Politecnico di Milano, Via Bonardi 9, Milano 20133

Received: February 28, 2011

Revised: May 31, 2011

Published: May 2012

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Abstract

For a semigroup $S(t):X\to X$ acting on a metric space $(X,d)$, we give a notion of global attractor based only on the minimality with respect to the attraction property. Such an attractor is shown to be invariant whenever $S(t)$ is asymptotically closed. As a byproduct, we generalize earlier results on the existence of global attractors in the classical sense.

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Mathematics Subject Classification: Primary: 34D45; Secondary: 47H20.

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References

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