Existência e semicontinuidade de atratores global, pullback e de trajetórias

Abstract

The mainly purpose of this paper is to study the asymptotic behaviour of abstract evolution equations. The first part of this work is dedicated to the attraction theory for univoque autonomous and nonautonomous problems and for multivoque autonomous problems. After that, we analyse the existence of the appropriate type of attractor for a reaction-diffusion equation (autonomous and with uniqueness property), a variation of the previous equation (which makes it no longer possible to ensure the uniqueness property) and a delayed differential equation (non-autonomous). For the two lasting equations, we also investigate the upper-semicontinuity of the families of the corresponding attractors.