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Attractors for semilinear wave equations with localized damping and external forces

To Fu Ma, ,Institute of Mathematical and Computer Sciences, University of São Paulo, São Carlos 13566-590, SP, Brazil, Paulo Nicanor Seminario-Huertas, ,Faculty of Engineering, University of Ricardo Palma, Lima, Peru
2020 Communications on Pure and Applied Analysis  

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This paper is concerned with long-time dynamics of semilinear wave equations defined on bounded domains of 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
more » ... uity 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. 2000 Mathematics Subject Classification. Primary: 35B41, 35L71, 35B33; Secondary: 35B40.
doi:10.3934/cpaa.2020097 fatcat:24zuuh4otndgnjgptfgy5sm5hu
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To Fu Ma, ,Institute of Mathematical and Computer Sciences, University of São Paulo, São Carlos 13566-590, SP, Brazil, Paulo Nicanor Seminario-Huertas, ,Faculty of Engineering, University of Ricardo Palma, Lima, Peru. "Attractors for semilinear wave equations with localized damping and external forces." Communications on Pure and Applied Analysis 19.4 (2020) 2219-2233