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

doi:10.1016/S0252-9602(18)30768-9

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

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. 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 SHE^1,2, Jinyan YIN³

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/Abstract

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:

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

李扬荣, 佘连兵, 尹金艳. EQUI-ATTRACTION AND BACKWARD COMPACTNESS OF PULLBACK ATTRACTORS FOR POINT-DISSIPATIVE GINZBURG-LANDAU EQUATIONS[J]. 数学物理学报(英文版), 2018, 38(2): 591-609.

Yangrong LI, Lianbing SHE, Jinyan YIN. EQUI-ATTRACTION AND BACKWARD COMPACTNESS OF PULLBACK ATTRACTORS FOR POINT-DISSIPATIVE GINZBURG-LANDAU EQUATIONS[J]. Acta mathematica scientia,Series B, 2018, 38(2): 591-609.

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

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

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