Time-dependent global attractors for the strongly damped wave equations with lower regular forcing term
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Published:2022-12-10
Issue:
Volume:
Page:1-20
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ISSN:1230-3429
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Container-title:Topological Methods in Nonlinear Analysis
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language:
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Short-container-title:TMNA
Author:
Mei Xinyu,Sun Tao,Xie Yongqin,Zhu Kaixuan
Abstract
In this paper, based on a new theoretical framework of
time-dependent global attractors (Conti, Pata and Temam \cite{CPT13}),
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.
Publisher
Uniwersytet Mikolaja Kopernika/Nicolaus Copernicus University
Subject
Applied Mathematics,Analysis