Convergences of asymptotically autonomous pullback attractors towards semigroup attractors

TL;DR

This paper investigates how pullback attractors in asymptotically autonomous systems converge to the global attractors of the limiting semigroups, using conditions of uniform boundedness instead of compactness.

Contribution

It introduces new convergence results for pullback attractors towards semigroup attractors under uniform boundedness conditions.

Findings

Both forward and backward convergence are established.

Convergence results are obtained without relying on uniform compactness.

The approach broadens understanding of attractor behavior in asymptotically autonomous systems.

Abstract

For pullback attractors of asymptotically autonomous dynamical systems we study the convergences of their components towards the global attractors of the limiting semigroups. We use some conditions of uniform boundedness of pullback attractors, instead of uniform compactness conditions used in the literature. Both forward convergence and backward convergence are studied.