具有结构阻尼的扩展型梁方程的时间依赖吸引子
The Time-Dependent Global Attractors for an Extensible Beam Equation with StructuralDamping
DOI: 10.12677/AAM.2023.125238, PDF, HTML, 下载: 136  浏览: 242  国家自然科学基金支持
作者: 郭 瑞, 汪 璇*：西北师范大学数学与统计学院，甘肃 兰州
关键词: 结构阻尼；收缩函数；时间依赖吸引子；扩展型梁方程；Structural Damping； Contraction Function； The Time-Dependent Attractors； Extensible Beam Equation
摘要: 本文研究了带有结构阻尼的扩展型梁方程在空间 Ht 中解的长时间动力学行为。 首先证明了非线性 项 f (u) 在次临界条件下方程解的适定性，再利用收缩函数的方法验证了解过程 {U (t, τ )} 的渐近 紧性，最后证得了时间依赖吸引子的存在性。
Abstract: This paper studies longtime behavior of solutions for an extensible beam equation with structural damping in the Ht space. In the first instance, we show that the global well-posedness of solutions for the equation with nonlinearity f (u) under subcritical condition. Moreover, the asymptotic compactness of the solution process {U (t, τ )} is proved by using the method of contraction function. Finally, the existence of the time-dependent global attractor is gained.
文章引用：郭瑞, 汪璇. 具有结构阻尼的扩展型梁方程的时间依赖吸引子[J]. 应用数学进展, 2023, 12(5): 2340-2363. https://doi.org/10.12677/AAM.2023.125238

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