欧米茄
吸引子
有界函数
物理
波动方程
数学物理
数学分析
组合数学
数学
量子力学
作者
Kaixuan Zhu,Tong Sun,Yongqin Xie
出处
期刊:Discrete and Continuous Dynamical Systems-series B
[American Institute of Mathematical Sciences]
日期:2022-10-28
卷期号:28 (5): 3160-3171
标识
DOI:10.3934/dcdsb.2022207
摘要
We examine the long-term behavior of strong solutions for the wave equation $ \varepsilon(t)u_{tt}-\Delta u_{t}-\Delta u+f(u) = g(x) $ and obtain the time-dependent attractor in $ \mathcal{H}_{t}^{1} = [H^{2}(\Omega)\cap H_{0}^{1}(\Omega)]\times H_{0}^{1}(\Omega) $. Moreover, the attractor is bounded in $ [H^{2}(\Omega)\cap H_{0}^{1}(\Omega)]\times[H^{2}(\Omega)\cap H_{0}^{1}(\Omega)] $.
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