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

Xu Ling; Xie Jingyi

doi:10.11714/acta.snus.ZR20260022

您当前的位置：

首页 >

文章列表页 >

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

Research articles | 更新时间：2026-10-20

- Long-time dynamics for a Kirchhoff beam equation with degenerate nonlocal strong damping
- Acta Scientiarum Naturalium Universitatis Sunyatseni Vol. 65, Issue 5, Pages: 147-158(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：26 May 2026，
  
  Published：25 September 2026
- 稿件说明：
移动端阅览
徐玲,谢婧怡.具有退化非局部强阻尼的Kirchhoff型梁方程的长时间动力学行为[J].中山大学学报(自然科学版)(中英文),2026,65(05):147-158.

Xu Ling,Xie Jingyi.Long-time dynamics for a Kirchhoff beam equation with degenerate nonlocal strong damping[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2026,65(05):147-158.
徐玲,谢婧怡.具有退化非局部强阻尼的Kirchhoff型梁方程的长时间动力学行为[J].中山大学学报(自然科学版)(中英文),2026,65(05):147-158. DOI： 10.11714/acta.snus.ZR20260022.

Xu Ling,Xie Jingyi.Long-time dynamics for a Kirchhoff beam equation with degenerate nonlocal strong damping[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2026,65(05):147-158. 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=120641193&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=120641155&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=120641170&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=120641185&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 asymptot

ic 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=120641171&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=120641156&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

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=120641218&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=120641157&type=

6.18066692

3.47133350

关键词

Keywords

references

马巧珍，孙春友，钟承奎， 2007 . 非线性梁方程强全局吸引子的存在性［J］. 数学物理学报（A辑）， 27 （ 5 ）： 941 - 948 .

Babin A V ， Vishik M I ， 1992 . Attractors of evolution equations ［M］. Amsterdam ： North-Holland .

Balakrishnan A V ， 1988 . A theory of nonlinear damping in flexible structures ［C］// The Proceedings of the Comcon Workshop on Stabilization of Flexible Structures/Montpellier ， France December 1987 .

Balakrishnan A V ， Taylor L W ， 1989 . Distributed parameter nonlinear damping models for flight structures ［C］// Proceedings of Damping ' 89 ： 8 - 10 February 1989 West Palm Beach， Florida .

Berger H M ， 1955 . A new approach to the analysis of large deflections of plates ［J］. J Appl Mech ， 22 （ 4 ）： 465 - 472 .

Cavalcanti M M ， Domingos Cavalcanti V N ， Jorge Silva M A ， et al ， 2021 . Stability for extensible beams with a single degenerate nonlocal damping of Balakrishnan-Taylor type ［J］. J Differ Equ ， 290 ： 197 - 222 .

Chepyzhov V V ， Vishik M I ， 2002 . Attractors for equations of mathematical physics ［M］. Providence ： American Mathematical Society .

Chueshov I ， Lasiecka I ， 2008 . Long-time behavior of second order evolution equations with nonlinear damping ［J］. Memoirs AMS ， 195 （ 912 ）： 1 - 178 .

Gomes Tavares E H ， Jorge Silva M A ， Narciso V ， et al ， 2023 . Dynamics of a class of extensible beams with degenerate and non-degenerate nonlocal damping ［J］. Adv Differ Equ ， 28 （ 7/8 ）： 685 - 752 .

Ma Q F ， Wang S H ， Zhong C K ， 2002 . Necessary and sufficient conditions for the existence of global attractors for semigroups and applications ［J］. Indiana Univ Math J ， 51 （ 6 ）： 1541 - 1570 .

Medeiros L A ， 1979 . On a new class of nonlinear wave equations ［J］. J Math Anal Appl ， 69 （ 1 ）： 252 - 262 .

Meng F J ， Wu J ， Zhao C X ， 2019 . Time-dependent global attractor for extensible Berger equation ［J］. J Math Anal Appl ， 469 （ 2 ）： 1045 - 1069 .

Silva M A J ， Narciso V ， Vicente A ， 2019 . On a beam model related to flight structures with nonlocal energy damping ［J］. Discrete Contin Dyn Syst B ， 24 （ 7 ）： 3281 - 3298 .

Sun Y ， Yang Z J ， 2022a . Attractors and their continuity for an extensible beam equation with rotational inertia and nonlocal energy damping ［J］. J Math Anal Appl ， 512 （ 2 ）： 126148 .

Sun Y ， Yang Z J ， 2022b . Strong attractors and their robustness for an extensible beam model with energy damping ［J］. Discrete Contin Dyn Syst B ， 27 （ 6 ）： 3101 - 3129 .

Woinowsky-Krieger S ， 1950 . The effect of an axial force on the vibration of hinged bars ［J］. J Appl Mech ， 17 （ 1 ）： 35 - 36 .

Yan S L ， Zhong C K ， 2025 . Well-posedness and strong attractors for a beam model with degenerate nonlocal strong damping ［J］. J Differ Equ ， 442 ： 113495 .

Yang L ， Wang X ， 2017 . Existence of attractors for the non-autonomous Berger equation with nonlinear damping ［J］. Electron J Differ Equ ， 2017（ 278 ）： 1 - 14 .

Yao X B ， Ma Q Z ， 2017 . Global attractors of the extensible plate equations with nonlinear damping and memory ［J］. J Funct Spaces ， 2017 （ 1 ）： 4896161 .

Zhong C K ， Yang M H ， Sun C Y ， 2006 . The existence of global attractors for the norm-to-weak continuous semigroup and application to the nonlinear reaction-diffusion equations ［J］. J Differ Equ ， 223 （ 2 ）： 367 - 399 .

Views

下载量

CSCD

Alert me when the article has been cited

提交

Tools

Publicity Resources

Turing-Hopf bifurcation of a minimal sediment model with diffusion

Water resource dynamics in China’s major river basins （1900-2100）： A Budyko equation-based analysis

The Holocene sedimentary and paleoenvironmental evolution in Hailing Bay， Guangdong

Effects of polycyclic aromatic hydrocarbons on the photosynthesis system of Raphidocelis subcapitata and transcriptional regulatory mechanisms

Simpson's rule-assisted infrared spectroscopic analysis of adenosine in Cordyceps sinensis

Related Author

No data

Related Institution

No data

Postal code：510275
Tel：020-84112585，84113223 Email：xuebaozr@mail.sysu.edu.cn
Technical support is provided by Beijing Founder electronics co., LTD 京ICP备09064830号-19 京公网安备11010802024621
It is recommended to read the content of this site in Chrome&IE9+. Please switch to extreme mode in browser 360.
Cookies We use cookies to help provide and enhance our service and tailor content. By continuing, you agree to the use of cookies.

⁰