数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (2): 591-609.doi: 10.1016/S0252-9602(18)30768-9

• 论文 • 上一篇    下一篇

EQUI-ATTRACTION AND BACKWARD COMPACTNESS OF PULLBACK ATTRACTORS FOR POINT-DISSIPATIVE GINZBURG-LANDAU EQUATIONS

李扬荣1, 佘连兵1,2, 尹金艳3   

  1. 1. School of Mathematics and Statistics, Southwest University, Chongqing 400715, China;
    2. Department of Mathematics, Liupanshui normal college, Liupanshui 553004, China;
    3. School of Mathematics and Information, China West Normal University, Nanchong 637002, China
  • 收稿日期:2016-09-30 修回日期:2017-08-04 出版日期:2018-04-25 发布日期:2018-04-25
  • 作者简介:Yangrong LI,E-mail:liyr@swu.edu.cn;Lianbing SHE,E-mail:shelianbing@163.com;Jinyan YIN,E-mail:yjy111@email.swu.edu.cn
  • 基金资助:

    Y. Li is supported by the National Natural Science Foundation of China (11571283) and L. She is supported by Natural Science Foundation of Guizhou Province (KY[2016]103).

EQUI-ATTRACTION AND BACKWARD COMPACTNESS OF PULLBACK ATTRACTORS FOR POINT-DISSIPATIVE GINZBURG-LANDAU EQUATIONS

Yangrong LI1, Lianbing SHE1,2, Jinyan YIN3   

  1. 1. School of Mathematics and Statistics, Southwest University, Chongqing 400715, China;
    2. Department of Mathematics, Liupanshui normal college, Liupanshui 553004, China;
    3. School of Mathematics and Information, China West Normal University, Nanchong 637002, China
  • Received:2016-09-30 Revised:2017-08-04 Online:2018-04-25 Published:2018-04-25
  • Supported by:

    Y. Li is supported by the National Natural Science Foundation of China (11571283) and L. She is supported by Natural Science Foundation of Guizhou Province (KY[2016]103).

摘要:

A new concept of an equi-attractor is introduced, and defined by the minimal compact set that attracts bounded sets uniformly in the past, for a non-autonomous dynamical system. It is shown that the compact equi-attraction implies the backward compactness of a pullback attractor. Also, an eventually equi-continuous and strongly bounded process has an equi-attractor if and only if it is strongly point dissipative and strongly asymptotically compact. Those results primely strengthen the known existence result of a backward bounded pullback attractor in the literature. Finally, the theoretical criteria are applied to prove the existence of both equi-attractor and backward compact attractor for a Ginzburg-Landau equation with some varying coefficients and a backward tempered external force.

关键词: Non-autonomous systems, point dissipative processes, pullback attractors, backward compact attractors, equi-attractors, Ginzburg-Landau equations

Abstract:

A new concept of an equi-attractor is introduced, and defined by the minimal compact set that attracts bounded sets uniformly in the past, for a non-autonomous dynamical system. It is shown that the compact equi-attraction implies the backward compactness of a pullback attractor. Also, an eventually equi-continuous and strongly bounded process has an equi-attractor if and only if it is strongly point dissipative and strongly asymptotically compact. Those results primely strengthen the known existence result of a backward bounded pullback attractor in the literature. Finally, the theoretical criteria are applied to prove the existence of both equi-attractor and backward compact attractor for a Ginzburg-Landau equation with some varying coefficients and a backward tempered external force.

Key words: Non-autonomous systems, point dissipative processes, pullback attractors, backward compact attractors, equi-attractors, Ginzburg-Landau equations