Generalized $\varphi$-pullback attractors for evolution processes and application to a nonautonomous wave equation

TL;DR

This paper introduces generalized $$-pullback attractors for evolution processes in metric spaces, establishing conditions for their existence and applying the theory to a nonautonomous wave equation.

Contribution

It defines a new class of pullback attractors with a rate function $$, providing existence conditions and demonstrating their application to a specific wave equation.

Findings

Established existence conditions for generalized $$-pullback attractors.

Introduced generalized polynomial pullback attractors.

Applied the theory to a nonautonomous wave equation.

Abstract

In this work we define the generalized $\varphi$-pullback attractors for evolution processes in complete metric spaces, which are compact and positively invariant families, such that they pullback attract bounded sets with a rate determined by a decreasing function $\varphi$ that vanishes at infinity. We find conditions under which a given evolution process has a generalized $\varphi$-pullback attractor, both in the discrete and in the continuous cases. We present a result for the special case of generalized polynomial pullback attractors, and apply it to obtain such an object for a nonautonomous wave equation.