波方程与欧拉伯努利板方程耦合系统的全局吸引子

数学物理学报 ›› 2023, Vol. 43 ›› Issue (4): 1179-1196.

波方程与欧拉伯努利板方程耦合系统的全局吸引子

彭青青^1,²(),张志飞^1,^2,^*()

¹华中科技大学数学与统计学院武汉 430074
²湖北省工程建模与科学计算重点实验室华中科技大学武汉 430074

收稿日期:2022-04-26 修回日期:2023-02-06 出版日期:2023-08-26 发布日期:2023-07-03
通讯作者: 张志飞 E-mail:pengqq@hust.edu.cn;zhangzf@hust.edu.cn
作者简介:彭青青，E-mail: pengqq@hust.edu.cn

Global Attractor for a Coupled System of Wave and Euler-Bernoulli Plate Equation with Boundary Weak Damping

Peng Qingqing^1,²(),Zhang Zhifei^1,^2,^*()

¹School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074
²Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan 430074

Received:2022-04-26 Revised:2023-02-06 Online:2023-08-26 Published:2023-07-03
Contact: Zhifei Zhang E-mail:pengqq@hust.edu.cn;zhangzf@hust.edu.cn

摘要/Abstract

摘要：

该文研究了黎曼流形上半线性波方程与欧拉伯努利板方程耦合系统的长时间性态, 该系统具有边界耗散结构. 在逃逸向量场存在性假设下利用乘子方法证明了原耦合系统全局紧吸引子的存在性, 该存在性与黎曼度量的曲率性质有关.

关键词: 全局吸引子, 波/板耦合, 几何乘子法, 非线性边界耗散.

Abstract:

In this paper, we consider the longtime behavior for a coupled system consisting of the semi-linear wave equation with nonlinear boundary dissipation and the Euler-Bernoulli plate equation on a Riemannian manifold. It is shown that the existence of global and compact attractors depends on the curvature properties of the metric on the manifold by using the multiplier method and the hypothesis of escape vector field.

Key words: Global attractor, Coupled wave/plate equation, Geometric multiplier method, Nonlinear boundary dissipation

中图分类号:

O231.4

彭青青,张志飞. 波方程与欧拉伯努利板方程耦合系统的全局吸引子[J]. 数学物理学报, 2023, 43(4): 1179-1196.

Peng Qingqing,Zhang Zhifei. Global Attractor for a Coupled System of Wave and Euler-Bernoulli Plate Equation with Boundary Weak Damping[J]. Acta mathematica scientia,Series A, 2023, 43(4): 1179-1196.

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