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 is the set of asymptotic states described by Z().
Jacson Simsen is supported by CAPES-Brazil. |