Attractors for semilinear wave equations with localized damping and external forces
| Autor: | Paulo N. Seminario-Huertas, To Fu Ma |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Physics
Current (mathematics) Dense set EQUAÇÕES DA ONDA Applied Mathematics 010102 general mathematics Mathematical analysis General Medicine Wave equation 01 natural sciences Exponential function 010101 applied mathematics Nonlinear system Mathematics - Analysis of PDEs Bounded function Attractor FOS: Mathematics Uniform boundedness Primary: 35B41 35L71 35B33 Secondary: 35B40 0101 mathematics Analysis Analysis of PDEs (math.AP) |
| Zdroj: | Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual) Universidade de São Paulo (USP) instacron:USP |
| Popis: | This paper is concerned with long-time dynamics of semilinear wave equations defined on bounded domains of \begin{document}$ \mathbb{R}^3 $\end{document} 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. |
| Databáze: | OpenAIRE |
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