Attractors for semilinear wave equations with localized damping and external forces
Analysis of PDEs
2021-02-25 v1
Abstract
This paper is concerned with long-time dynamics of semilinear wave equations defined on bounded domains of 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.
Keywords
Cite
@article{arxiv.1905.03285,
title = {Attractors for semilinear wave equations with localized damping and external forces},
author = {To Fu Ma and Paulo N. Seminario-Huertas},
journal= {arXiv preprint arXiv:1905.03285},
year = {2021}
}