带有时滞项的超三次弱阻尼波方程一致吸引子的存在性

数学物理学报 ›› 2022, Vol. 42 ›› Issue (1): 86-102.

带有时滞项的超三次弱阻尼波方程一致吸引子的存在性

朱凯旋^1,*(),谢永钦²(),梅鑫钰³(),邓习军¹()

¹ 湖南文理学院数理学院&洞庭湖生态经济区建设与发展湖南省协同创新中心湖南常德 415000
² 长沙理工大学数学与统计学院长沙 410114
³ 深圳大学数学与统计学院广东深圳 518060

收稿日期:2020-07-27 出版日期:2022-02-26 发布日期:2022-02-23
通讯作者: 朱凯旋 E-mail:zhukx12@163.com;xieyq@csust.edu.cn;meixy@szu.edu.cn;xijundeng@126.com
作者简介:谢永钦, E-mail: xieyq@csust.edu.cn|梅鑫钰, E-mail: meixy@szu.edu.cn|邓习军, E-mail: xijundeng@126.com
基金资助:
湖南省自然科学基金(2018JJ2272);湖南省教育厅科学研究基金(20C1263);湖南文理学院科技创新团队项目（数值计算和随机过程及应用）

Uniform Attractors for the Sup-Cubic Weakly Damped Wave Equations with Delays

Kaixuan Zhu^1,*(),Yongqin Xie²(),Xinyu Mei³(),Xijun Deng¹()

¹ College of Mathematics and Physics Science, Hunan University of Arts and Science & Hunan Province Cooperative Innovation Center for the Construction and Development of Dongting Lake Ecological Economic Zone, Hunan Changde 415000
² School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha 410114
³ School of Mathematics and Statistics, Shenzhen University, Guangdong Shenzhen 518060

Received:2020-07-27 Online:2022-02-26 Published:2022-02-23
Contact: Kaixuan Zhu E-mail:zhukx12@163.com;xieyq@csust.edu.cn;meixy@szu.edu.cn;xijundeng@126.com
Supported by:
the NFS of Hunan Province(2018JJ2272);the Scientific Research Fund of Hunan Provincial Education Department(20C1263);the Hunan University of Arts and Science(STIT): Numerical Calculation and Stochastic Process with Their Applications

摘要/Abstract

摘要：

该文考虑带有时滞项的弱阻尼波方程一致吸引子的存在性，其中非线性项的增长次数大于3而小于5.通过构造能量泛函并结合收缩函数方法得到过程$U_{g}(t, \tau)$，$g\in{\cal H}(g_{0})$在$C_{H^{1}_{0}(\Omega)}\times C_{L^{2}(\Omega)}$中一致吸引子的存在性.

关键词: 弱阻尼波方程, 时滞, 一致吸引子

Abstract:

In this paper, we consider the weakly damped wave equations with delays and sup-cubic nonlinearity. We prove the existence of the uniform attractors in $C_{H_{0}^{1}(\Omega)}\times C_{L^{2}(\Omega)}$ by constructing the energy functional and combining with the idea of contractive functions..

Key words: Weakly damped wave equations, Delays, Uniform attractors

中图分类号:

O193

朱凯旋,谢永钦,梅鑫钰,邓习军. 带有时滞项的超三次弱阻尼波方程一致吸引子的存在性[J]. 数学物理学报, 2022, 42(1): 86-102.

Kaixuan Zhu,Yongqin Xie,Xinyu Mei,Xijun Deng. Uniform Attractors for the Sup-Cubic Weakly Damped Wave Equations with Delays[J]. Acta mathematica scientia,Series A, 2022, 42(1): 86-102.

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