Exponential stability of solutions for stochastic elastic system with damping and infinite delay

ZHANG Xiaoyun; FAN Hongxia

doi:10.13471/j.cnki.acta.snus.ZR20240126

您当前的位置：

首页 >

文章列表页 >

Exponential stability of solutions for stochastic elastic system with damping and infinite delay

Research articles | 更新时间：2025-11-14

- Exponential stability of solutions for stochastic elastic system with damping and infinite delay
- Acta Scientiarum Naturalium Universitatis Sunyatseni Vol. 64, Issue 2, Pages: 170-178(2025)
- 作者机构：
  
  兰州交通大学数理学院，甘肃兰州 730070
- 作者简介：
- 基金信息：
- DOI：10.13471/j.cnki.acta.snus.ZR20240126
  CLC： O175.15
- Received：21 April 2024，
  
  Accepted：04 October 2024，
  
  Published Online：03 January 2025，
  
  Published：15 March 2025
- 稿件说明：
移动端阅览
张小云,范虹霞.具有阻尼和无穷时滞的随机弹性系统解的指数稳定性[J].中山大学学报(自然科学版)(中英文),2025,64(02):170-178.

ZHANG Xiaoyun,FAN Hongxia.Exponential stability of solutions for stochastic elastic system with damping and infinite delay[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2025,64(02):170-178.
张小云,范虹霞.具有阻尼和无穷时滞的随机弹性系统解的指数稳定性[J].中山大学学报(自然科学版)(中英文),2025,64(02):170-178. DOI： 10.13471/j.cnki.acta.snus.ZR20240126.

ZHANG Xiaoyun,FAN Hongxia.Exponential stability of solutions for stochastic elastic system with damping and infinite delay[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2025,64(02):170-178. DOI： 10.13471/j.cnki.acta.snus.ZR20240126.

摘要

研究在Hilbert空间中具有阻尼和无穷时滞的随机弹性系统mild解的存在唯一性和指数稳定性，利用算子半群理论、公理化相空间的性质及随机分析，获得了所研究问题mild解的存在唯一性和均方指数稳定性，丰富和发展了阻尼弹性系统已有的结果.

Abstract

The existence，uniqueness and exponential stability of mild solutions of stochastic elastic systems with damping and infinite delay are studied in Hilbert spaces. By using the theory of operator semigroups， properties of axiomatic phase space and stochastic analysis， the existence and uniqueness of mild solution and the exponential stability in mean square are obtained， the existing results of damping elastic systems are enriched and developed.

关键词

Keywords

references

李永祥， 1997 . 关于抽象强阻尼波方程的指数稳定性［J］. 数学年刊A辑， 18 （ 3 ）： 299 - 306 .

CHEN G ， RUSSELL D L ， 1982 . A mathematical model for linear elastic systems with structural damping ［J］. Quart Appl Math ， 39 （ 4 ）： 433 - 454 .

CHEN G ， van GAANS O ， LUNEL S V ， 2018 . Existence and exponential stability of a class of impulsive neutral stochastic partial differential equations with delays and Poisson jumps ［J］. Stat Probab Lett ， 141 ： 7 - 18 .

DIAGANA T ， 2017 . Well-posedness for some damped elastic systems in Banach spaces ［J］. Appl Math Lett ， 71 ： 74 - 80 .

FAN H X ， GAO F ， 2014a . Asymptotic stability of solutions to elastic systems with structural damping ［J］. Electron J Differ Equ ， 245 ： 1 - 9 .

FAN H X ， LI Y X ， 2014b . Analyticity and exponential stability of semigroups for the elastic systems with structural damping in Banach spaces ［J］. J Math Anal Appl ， 410 （ 1 ）： 316 - 322 .

FAN H X ， LI Y X ， 2014c . Monotone iterative technique for the elastic systems with structural damping in Banach spaces ［J］. Comput Math Appl ， 68 （ 3 ）： 384 - 391 .

GOU H D ， MA W ， 2023 . A study on decay mild solutions for damped elastic systems in Banach spaces ［J］. Monasth Für Math ， 202 （ 3 ）： 515 - 539 .

GOU H D ， YANG H ， 2024 . Monotone iterative technique for delay elastic systems in ordered Banach space ［J］. Appl Anal ， 103 （ 13 ）： 2390 - 2409 .

HUANG F L ， 1985 . On the holomorphic property of the semigroup associated with linear elastic systems with structural damping ［J］. Acta Math Sci ， 5 （ 3 ）： 271 - 277 .

HUANG F L ， 1986 . A problem for linear elastic systems with structural damping ［J］. Acta Math Sci ， 6 ： 107 - 113 .

HALE J K ， KATO J ， 1978 . Phase space for retarded equations with infinite delay ［J］. Funkc Ekvacioj-Ser I ， 21 （ 1 ）： 11 - 41 .

HALE J K ， LUNEL S M V ， 1993 . Introduction to functional differential equations ［M］. New York ： Springer .

LUONG V T ， TUNG N T ， 2020 . Exponential decay for elastic systems with structural damping and infinite delay ［J］. Appl Anal ， 99 （ 1 ）： 13 - 28 .

MASSATT P ， 1983 . Limiting behavior for strongly damped nonlinear wave equations ［J］. J Differ Equ ， 48 （ 3 ）： 334 - 349 .

PAZY A ， 1983 . Semigroups of linear operators and applications to partial differential equations ［M］. New York ： Springer .

WEI M ， LI Y X ， LI Q ， 2022 . Positive mild solutions for damped elastic systems with delay and nonlocal conditions in ordered Banach space ［J］. Qual Theory Dyn Syst ， 21 （ 4 ）： 128 .

Views

下载量

CSCD

Alert me when the article has been cited

提交

Tools

Publicity Resources

No data

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