非线性Ginzburg-Landau方程的拉回吸引子

曲靖师范学院学报 ›› 2016, Vol. 35 ›› Issue (6): 7-9.

非线性Ginzburg-Landau方程的拉回吸引子

张凤,姜金平^*,王艳,严建军

延安大学数学与计算机科学学院,陕西延安 716000

收稿日期:2016-10-24 出版日期:2016-11-26
通讯作者: 姜金平,延安大学数学与计算机科学学院教授,主要从事无穷维动力系统研究
作者简介:张凤,延安大学数学与计算机科学学院硕士研究生,主要从事无穷维动力系统研究.
基金资助:
2016年陕西省教育厅科研项目“几类非线性动力系统解得渐近性研究”(16JK1856);延安大学校级科研项目“一类非线性系统的动力学行为研究”(YD2016-05).

Pullback Attractor for the Nonlinear Ginzburg - Landau Equation

Zhang Feng, Jiang Jinping, Wang Yan, Yan Jianjun

School of Mathematics and Computer Science,Yan'an University, Yan'an Shanxi 716000,P. R. China

Received:2016-10-24 Published:2016-11-26

摘要/Abstract

摘要： 研究非线性Ginzburg-Landau方程中拉回D-吸引子的存在性, 通过证明其满足拉回吸收集, 然后利用拉回条件C, 证明Ginzburg-Landau方程存在拉回吸引子.

关键词: Ginzburg-Landau方程, 拉回条件C, 拉回吸引子

Abstract: The existence of the pullback D-attractor in the nonlinear Ginzburg-Landau equation is studied by proving that it satisfies the pull-back absorption set and the pull-back condition C is used to prove the existence of pullback attractor for the Ginzburg-Landau equation.

Key words: Ginzburg-Landau Equation, pull-back condition C, Pullback attractors

中图分类号:

O175.29

张凤,姜金平,王艳,严建军. 非线性Ginzburg-Landau方程的拉回吸引子[J]. 曲靖师范学院学报, 2016, 35(6): 7-9.

Zhang Feng, Jiang Jinping, Wang Yan, Yan Jianjun. Pullback Attractor for the Nonlinear Ginzburg - Landau Equation[J]. JOURNAL OF QUJING NORMAL UNIVERSITY, 2016, 35(6): 7-9.

参考文献

[1]陈兆蕙,李泽华.3维非线性复Ginzburg-Landau方程的同宿波解[J].徐州师范大学学报:自然科学版,2012(1):14-17.
[2]Ghidaglia J M,Heron B. Dimension of the attractor associated to the Ginzburg-Landau Equation[J]. Phys D,1987(7):282-287.
[3]Crauel H,Flandoli F. Attractors for random dynamical systems probab[J].Theory Related Fields,1994,100:365-393.
[4]Crauel H, Debussche A, Flandoli F. Random attractors[J].Dynamics Differential Equations,1997,9:307-341.
[5]Kloeden P E,Schmalfuss B. Non-autonomous systems cocycle attractors and variable time-step discretization,Numer[J].Algorithms,1997,14:141-152.
[6]高洪俊,郭柏灵.广义Ginzburg-Landau方程的有限维行为[J].自然科学进展,1994(4):423-434.
[7]李向正,张金良,王明亮.Ginzburg-Landau方程的一种解法[J].河南科技大学学报:自然科学版,2004(6):78-81.
[8]曹镇潮,王碧祥,郭柏灵.二维具导数项Ginzburg-Landau方程整体解的存在性[J].科学通报,1997 (17):1809-1812.
[9]Huang J,Dai Z D .Exponential Attactor for the Derivative Two-dimensional Ginzburg-Landau EquaTi-on in Banach Spaces[J].Chinese Journal of Engineering Mathematics,2004,6:443-447.
[10]刘常福,戴正德.二维广义Ginzburg-Landau方程在Banach空间的指数吸引子[J].应用数学学报,2005(1):134-142.
[11]Marn-Rubio P, Real J. On the relation between two different concepts of pullback attractors for non-autono-mous dynamical systems[J]. Nonlinear Analysis, 2009(9): 3956-3963.
[12]Garca-Luengo J, Marn-Rubio P. Real J.Pullback attractors in V for non-autonomous 2D-Navier-Stokes equ-ations and their tempered behaviour[J]. Journal of Differential Equations, 2012(8): 4333-4356.
[13]李栋龙,郭柏灵,刘旭红.三维复Ginzburg-Landau方程的整体解的存在唯一性[J].高校应用数学学报,2004(4):409-416.