Asymptotic almost-equivalence of abstract evolution systems

TL;DR

This paper investigates the long-term behavior of almost-orbits in abstract evolution systems within Banach spaces, establishing various convergence properties and analyzing almost-stationary points.

Contribution

It provides new results on the asymptotic convergence and behavior of almost-orbits in Banach space evolution systems, including weak and strong convergence analysis.

Findings

Convergence of almost-orbits in Banach spaces

Analysis of almost-stationary points

Results hold with or without Lipschitz assumptions

Abstract

We study the asymptotic behavior of almost-orbits of abstract evolution systems in Banach spaces with or without a Lipschitz assumption. In particular, we establish convergence, convergence in average and almost-convergence of almost-orbits both for the weak and the strong topologies based on the behavior of the orbits. We also analyze the set of almost-stationary points.