# Attractors for semilinear wave equations with localized damping and external forces

## TL;DR

This paper investigates the long-term behavior of semilinear wave equations with localized damping and external forces, establishing uniform boundedness, continuity, and existence of generalized exponential attractors, advancing understanding of their dynamics.

## Contribution

It introduces new results on the uniform boundedness, parameter continuity, and generalized exponential attractors for wave equations with localized damping.

## Key findings

- Uniform boundedness of attractors with respect to forcing parameter
- Continuity of attractors in a residual dense set of parameters
- Existence of generalized exponential attractors

## Abstract

This paper is concerned with long-time dynamics of semilinear wave equations defined on bounded domains of $\mathbb{R}^3$ with cubic nonlinear terms and locally distributed damping. The existence of regular finite-dimensional global attractors established by Chueshov, Lasiecka and Toundykov (2008) reflects a good deal of the current state of the art on this matter. Our contribution is threefold. First, we prove uniform boundedness of attractors with respect to a forcing parameter. Then, we study the continuity of attractors with respect to the parameter in a residual dense set. Finally, we show the existence of generalized exponential attractors. These aspects were not previously considered for wave equations with localized damping.