Acta mathematica scientia,Series A ›› 2020, Vol. 40 ›› Issue (5): 1341-1353.

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Pullback Attractors for the Complex Ginzburg-Landau Equations with Delays

Kaixuan Zhu1,*(),Yongqin Xie2(),Feng Zhou3(),Xijun Deng1()   

  1. 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)

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

CLC Number: 

  • O193
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