Estimate of the attractive velocity of attractors for some dynamical systems

TL;DR

This paper establishes a theoretical framework for estimating the attractive velocity of polynomial attractors in infinite-dimensional dynamical systems, with applications to certain wave equations featuring nonlocal damping.

Contribution

It introduces an abstract theorem on polynomial attractors and their attractive velocity, then applies it to wave equations with nonlocal damping and anti-damping.

Findings

Proved existence of polynomial attractors in specified systems

Derived concrete estimates for their attractive velocity

Applied results to wave equations with nonlocal damping

Abstract

In this paper, we first prove an abstract theorem on the existence of polynomial attractors and the concrete estimate of their attractive velocity for infinite-dimensional dynamical systems, then apply this theorem to a class of wave equations with nonlocal weak damping and anti-damping in case that the nonlinear term~$f$~is of subcritical growth.