Hongyong Cui (University Southwest of Chongqing), José A. Langa (University of Sevilla), Yangrong Li (University Southwest of Chongqing) and José Valero (University Miguel Hernández of Elche).
Abstract. In this paper we study cocycle attractors, pullback attractors and uniform attractors for multi-valued non-autonomous dynamical systems.We first consider the relationship between the three attractors and find that, under suitable conditions, they imply each other. Then, for generalized dynamical systems, we find that these attractors can be characterized by complete trajectories, which implies that the uniform attractor is lifted invariant, though it has no standard invariance by definition. Finally, we study both upper and lower semi-continuity of these attractors. A weak equi-attraction method is introduced to study the lower semi continuity, and we show with an example the advantages of this method. A reaction-diffusion system and a scalar ordinary differential inclusion are studied as applications.
Keywords. Multi-valued dynamical systems; Pullback attractor; Uniform attractor; Lifted invariance; Lower semi-continuity; Weak equi-attraction