Long-time dynamics for a Kirchhoff beam equation with degenerate nonlocal strong damping

Xu Ling; Xie Jingyi

doi:10.11714/acta.snus.ZR20260022

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Long-time dynamics for a Kirchhoff beam equation with degenerate nonlocal strong damping

更新时间：2026-05-21

- Long-time dynamics for a Kirchhoff beam equation with degenerate nonlocal strong damping
- Acta Scientiarum Naturalium Universitatis Sunyatseni Pages: 1-12(2026)
- 作者机构：
  
  西北师范大学数学与统计学院，甘肃兰州 730070
- 作者简介：
- 基金信息：
- DOI：10.11714/acta.snus.ZR20260022
  CLC： O175.29
- Received：15 January 2026，
  
  Revised：2026-04-12，
  
  Accepted：21 April 2026，
  
  Online First：19 May 2026，
- 稿件说明：
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Xu Ling, Xie Jingyi. Long-time dynamics for a Kirchhoff beam equation with degenerate nonlocal strong damping[J/OL]. Acta Scientiarum Naturalium Universitatis Sunyatseni, 2026, 1-12.
DOI：

Xu Ling, Xie Jingyi. Long-time dynamics for a Kirchhoff beam equation with degenerate nonlocal strong damping[J/OL]. Acta Scientiarum Naturalium Universitatis Sunyatseni, 2026, 1-12. DOI： 10.11714/acta.snus.ZR20260022.

摘要

研究了一类具有退化非局部强阻尼的Kirchhoff型梁方程解的存在唯一性，全局吸引子与强全局吸引子的存在性. 首先，应用Faedo-Galerkin逼近和插值不等式证明了弱解的存在唯一性；其次，通过构造有界吸收集，证明解半群的渐近紧性，从而得到系统在拓扑空间

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=108702616&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=108702602&type=

2.70933342

2.37066650

存在全局吸引子；最后利用范数到弱连续半群理论和条件（C），证明了系统在强拓扑空间

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=108702592&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=108702581&type=

5.67266655

3.21733332

存在全局吸引子.

Abstract

The existence and uniqueness of solutions，as well as the existence of global attractors and strong global attractors are investigated for a class of Kirchhoff-type beam equations with degenerate nonlocal strong damping. Firstly， we establish the existence and uniqueness of weak solutions by employing the Faedo-Galerkin approximation along with interpolation inequalities. Secondly， by constructing a bounded absorbing set，we establish the asymptotic compactness of the solution semigroup， and thereby obtain the existence of a global attractor in the topological space

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=108702617&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=108702603&type=

3.13266683

2.79399991

. Finally， we apply the norm-to-weak continuous semigroup theory and condition （C）， to show that the system also has a global attractor in the stronger topological space

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6.18066692

3.47133350

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references

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