2022 Time-dependent global attractors for the strongly damped wave equations with lower regular forcing term
Xinyu Mei, Tao Sun, Yongqin Xie, Kaixuan Zhu
Topol. Methods Nonlinear Anal. 60(2): 653-672 (2022). DOI: 10.12775/TMNA.2022.022

Abstract

In this paper, based on a new theoretical framework of time-dependent global attractors (Conti, Pata and Temam [8]), we consider the strongly damped wave equations $\varepsilon(t)u_{tt}-\Delta u_{t}-\Delta u+f(u)=g(x)$ and establish the existence of attractors in $\mathcal{H}_{t}=H_{0}^{1}(\Omega)\times L^{2}(\Omega)$ and $\mathcal{V}_{t}=H_{0}^{1}(\Omega)\times H_{0}^{1}(\Omega)$, respectively.

Citation

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Xinyu Mei. Tao Sun. Yongqin Xie. Kaixuan Zhu. "Time-dependent global attractors for the strongly damped wave equations with lower regular forcing term." Topol. Methods Nonlinear Anal. 60 (2) 653 - 672, 2022. https://doi.org/10.12775/TMNA.2022.022

Information

Published: 2022
First available in Project Euclid: 10 December 2022

MathSciNet: MR4563252
zbMATH: 1509.35063
Digital Object Identifier: 10.12775/TMNA.2022.022

Keywords: critical exponential growth , Strongly damped wave equations , time-dependent global attractors

Rights: Copyright © 2022 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.60 • No. 2 • 2022
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