Monotone Multivalued Nonautonomous Dynamical Systems

TL;DR

This paper investigates nonautonomous multivalued semiflows, characterizing their attractors and bounds, and extends existing results to this framework, with applications to partial differential inclusions.

Contribution

It generalizes previous results on autonomous and nonautonomous flows to multivalued semiflows, providing bounds and continuity properties of attractors.

Findings

Characterization of attractor bounds as complete trajectories.

Extension of results to nonautonomous multivalued systems.

Proven upper semicontinuity of attractors with asymptotic convergence.

Abstract

This paper is devoted to the study of nonautonomous multivalued semiflows and their associated pullback attractors. For this kind of dynamical systems we are able to characterize the upper and lower bounds of the attractor as complete trajectories belonging to the attractor, so that all the internal dynamics is confined in this region, which can be described as an interval due to the orderly nature of the processes. Thus, we are able to generalize to this framework previous general results in literature for autonomous multivalued flows or nonautonomous differential equations. We apply our results to a partial differential inclusion with a nonautonomous term, also proving the upper semicontinuity dependence of pullback and global attractors when the time dependent term asymptotically converges to an autonomous multivalued term.