非线性阻尼波方程在R3上的时间依赖吸引子

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非线性阻尼波方程在R3上的时间依赖吸引子
Time-Dependent Attractor of Nonlinear Damping Wave Equation on R3

DOI: 10.12677/AAM.2023.1210437, PDF, 下载: 173 浏览: 212 国家自然科学基金支持
作者: 王兴慧：西北师范大学，数学与统计学院，甘肃兰州
关键词: 时间依赖吸引子；非线性阻尼；压缩函数；Time-Dependent Attractor； Nonlinear Damping； Contractive Functions

摘要: 基于时间依赖空间中的吸引子理论，本文研究了无界域上带有非线性阻尼的波方程解的长时间行为。利用压缩函数方法和一些估计技巧证明了过程的渐近紧性，进而得到了时间依赖吸引子的存在性。

Abstract: Based on the attractor theory in time-dependent spaces, we consider long-time be- havior of solutions for the wave equation with nonlinear damping on the unbounded domain. We prove the asymptotic compactness of the process by using the contrative functions and some detailed estimates, thus the existence of time-dependent attractors is proved.

文章引用：王兴慧. 非线性阻尼波方程在R3上的时间依赖吸引子[J]. 应用数学进展, 2023, 12(10): 4456-4466. https://doi.org/10.12677/AAM.2023.1210437

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