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April  2020, 19(4): 2219-2233. doi: 10.3934/cpaa.2020097

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

 1 Institute of Mathematical and Computer Sciences, University of São Paulo, São Carlos 13566-590, SP, Brazil 2 Faculty of Engineering, University of Ricardo Palma, Lima, Peru

*Corresponding author. Current affiliation: Department of Mathematics, University of Brasília, Brasília 70910-900, DF, Brazil

Dedicated to Professor Tomás Caraballo on occasion of his Sixtieth Birthday

Received  May 2019 Revised  September 2019 Published  January 2020

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.

Citation: To Fu Ma, Paulo Nicanor Seminario-Huertas. Attractors for semilinear wave equations with localized damping and external forces. Communications on Pure & Applied Analysis, 2020, 19 (4) : 2219-2233. doi: 10.3934/cpaa.2020097
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##### References:
The control region $\omega$ satisfies (GCC). Any ray of geometric optics inside $\Omega$ hits $\omega$
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