| 具结构阻尼的耦合梁方程组在非线性边界条件下的吸引子 |
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| 引用本文： | 张婷,张建文.具结构阻尼的耦合梁方程组在非线性边界条件下的吸引子[J].应用数学和力学,2021,42(1):102-112. |
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| 作者姓名： | 张婷 张建文 |
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| 作者单位： | 太原理工大学 数学系, 太原 030024 |
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| 基金项目： | 国家自然科学基金(11872264) |
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| 摘 要： | 研究了具有转动惯量和结构阻尼的耦合梁方程组在非线性边界条件下的吸引子.首先通过Faedo-Galerkin方法证明了整体解的存在唯一性,其次证明了系统存在有界吸收集和半群的渐近光滑性,最后得到了全局吸引子的存在.
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| 关 键 词： | 耦合梁 非线性边界条件 整体解 全局吸引子 |
| 收稿时间： | 2020-03-20 |
Attractors of Coupled Beam Equations With Structural Damping Under Nonlinear Boundary Conditions |
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| Institution: | College of Mathematics, Taiyuan University of Technology, Taiyuan 030024, P.R.China |
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| Abstract: | Attractors of the system of coupled beam equations with rotational inertia and structural damping under nonlinear boundary conditions were studied. Firstly, the existence and uniqueness of the global solution were proved by means of the Faedo-Galerkin method. Secondly, the existence of the bounded absorbing set in the system and the asymptotic smoothness of the related solution semigroup were also proved. Finally, the existence of the global attractor was given. |
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