带有时滞项的复Ginzburg-Landau方程的拉回吸引子

数学物理学报 ›› 2020, Vol. 40 ›› Issue (5): 1341-1353.

带有时滞项的复Ginzburg-Landau方程的拉回吸引子

朱凯旋^1,*(),谢永钦²(),周峰³(),邓习军¹()

¹ 洞庭湖生态经济区建设与发展湖南省协同创新中心&湖南文理学院数理学院湖南常德 415000
² 长沙理工大学数学与统计学院长沙 410114
³ 中国石油大学(华东) 山东青岛 266580

收稿日期:2019-02-27 出版日期:2020-10-26 发布日期:2020-11-04
通讯作者: 朱凯旋 E-mail:zhukx12@163.com;xieyq@csust.edu.cn;zhoufeng13@upc.edu.cn;xijundeng@126.com
作者简介:谢永钦, E-mail:xieyq@csust.edu.cn|周峰, E-mail:zhoufeng13@upc.edu.cn|邓习军, E-mail:xijundeng@126.com
基金资助:
国家自然科学基金(11601522);中央高校基础研究基金(17CX02036A);湖南省自然科学基金基金(2018JJ2416);湖南省自然科学基金基金(2018JJ2272);湖南文理学院博士科研启动基金(16BSQD04);湖南文理学院博士科研启动基金(16BSQD13)

Pullback Attractors for the Complex Ginzburg-Landau Equations with Delays

Kaixuan Zhu^1,*(),Yongqin Xie²(),Feng Zhou³(),Xijun Deng¹()

¹ Hunan Province Cooperative Innovation Center for the Construction and Development of Dongting Lake Ecological Economic Zone, College of Mathematics and Physics, Hunan University of Arts and Science, Hunan Changde 415000
² School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha 410114
³ College of Science, China University of Petroleum(East China), Shandong Qingdao 266580

Received:2019-02-27 Online:2020-10-26 Published:2020-11-04
Contact: Kaixuan Zhu E-mail:zhukx12@163.com;xieyq@csust.edu.cn;zhoufeng13@upc.edu.cn;xijundeng@126.com
Supported by:
the NSFC(11601522);the Fundamental Research Funds for the Central Universities(17CX02036A);the NSF of Hunan Province(2018JJ2416);the NSF of Hunan Province(2018JJ2272);the Doctoral Research Fund of Hunan University of Arts and Science(16BSQD04);the Doctoral Research Fund of Hunan University of Arts and Science(16BSQD13)

摘要/Abstract

摘要：

该文考虑带有时滞项的复Ginzburg-Landau方程解的适定性和拉回吸引子的存在性，其中非线性项满足任意$p-1$（$p$>2）次多项式增长.利用收缩函数方法验证解过程$\{U（t，\tau）\}_{t\geq\tau}$的紧性，得到$C_{L^{2}（\Omega）}$中拉回吸引子的存在性.

关键词: 复Ginzburg-Landau方程, 时滞, 拉回吸引子

Abstract:

In this paper, we consider the complex Ginzburg-Landau equations with hereditary effects and the nonlinear term satisfying the polynomial growth of arbitrary $p-1$ $(p>2)$ order. We analyze the well-posedness of solutions and prove the existence of the pullback attractors in $C_{L^{2}(\Omega)}$ by applying the contractive functions method.

Key words: Complex Ginzburg-Landau equations, Delays, Pullback attractors

中图分类号:

O193

朱凯旋,谢永钦,周峰,邓习军. 带有时滞项的复Ginzburg-Landau方程的拉回吸引子[J]. 数学物理学报, 2020, 40(5): 1341-1353.

Kaixuan Zhu,Yongqin Xie,Feng Zhou,Xijun Deng. Pullback Attractors for the Complex Ginzburg-Landau Equations with Delays[J]. Acta mathematica scientia,Series A, 2020, 40(5): 1341-1353.

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