Abstract
In this paper we extend results from Semigroup Theory on existence and characterization of attractors in order to include multivalued semigroups T(t) defined by generalized semiflows . In particular we show that, if is continuous, possesses a Lyapunov function, and has a global attractor which is maximal compact invariant, then = W u(Z()), where Z() is the stationary solutions set and W u(Z()) is the unstable set of Z(). We introduce the -attractor concept which does not enjoy any uniformity on time of attraction and we prove, under suitable conditions, that the global -attractor \(\widehat{N}\) is the set of asymptotic states described by Z().
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Jacson Simsen is supported by CAPES-Brazil.
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Simsen, J., Gentile, C.B. On Attractors for Multivalued Semigroups Defined by Generalized Semiflows. Set-Valued Anal 16, 105–124 (2008). https://doi.org/10.1007/s11228-006-0037-1
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DOI: https://doi.org/10.1007/s11228-006-0037-1