带附加噪声的随机广义2DGinzburg-Landau方程的渐进行为

李栋龙; 郭柏灵

doi:10.3879/j.issn.1000-0887.2009.08.001

带附加噪声的随机广义2DGinzburg-Landau方程的渐进行为

doi: 10.3879/j.issn.1000-0887.2009.08.001

李栋龙¹,
郭柏灵²

1.
广西工学院信息与计算科学系,广西柳州 545006;2.北京应用物理与计算数学研究所,北京 100081

基金项目: 国家自然科学基金资助项目(10661023);广西省自然科学基金资助项目(0832065);广西优秀人才资助计划资助项目

详细信息

作者简介:
李栋龙(1964- ),男,广东人,教授,博士(联系人.E-mail:lidl@21cn.com).

中图分类号: O175
计量
- 文章访问数: 1734
- HTML全文浏览量: 192
- PDF下载量: 830
- 被引次数: 0
出版历程
- 收稿日期: 2008-02-19
- 修回日期: 2009-07-02
- 刊出日期: 2009-08-15

Asymptotic Behavior of the 2D Generalized Stochastic Ginzburg-Landau Equation With Additive Noise

LI Dong-long¹,
GUO Bo-ling²

1.
Department of Information and Computing Science, Guangxi University of Technology, Liuzhou, Guangxi 545006, P. R. China;

摘要

摘要: 考虑带附加噪声的随机广义2D Ginzburg-Landau方程．通过先验估计的方法，随机动力系统的紧性得到证明，进一步验证了该随机动力系统在H10存在随机整体吸引子．
- 随机广义2D Ginzburg-Landau方程 /
- 随机动力系统 /
- 随机整体吸引子
Abstract: The 2D generalized stochastic Ginzburg-Landau equation with additive noise is considered. The compactness of the random dynamical system was established by a priori estimates method, which shows that the random dynamical system possesses a random attractor in H₀¹
- 2D generalized stochastic Ginzburg-Landau equation /
- random dynamical system /
- random attractor

HTML全文

参考文献(14)

[1]	Doering C, Gibbon J D, holm D, et al. Low-dimensional behavior in the complex Ginzburg-Landau equation[J].Nonlinearity,1988,1(2):279-309. doi: 10.1088/0951-7715/1/2/001
[2]	Ghidaglia J-M,Héron B.Dimension of the attractor associated to the Ginzburg-Landau equation[J].Physica D,1987,28(3):282-304. doi: 10.1016/0167-2789(87)90020-0
[3]	Bartuccelli M,Constantin P,Doering C,et al.On the possibility of soft and hard turbulence in the complex Ginzburg-Landau equation[J].Physica D,1990,44(3):421-444. doi: 10.1016/0167-2789(90)90156-J
[4]	Doering C R, Gibbon J D, Levermore C D. Weak and strong solutions of the complex Ginzburg-Landau equation[J].Physica D,1994,71(3):285-318. doi: 10.1016/0167-2789(94)90150-3
[5]	Levermore C D,Oliver M.The Complex Ginzburg-Landau Equation as a Model Problem[M].Lectures in Applied Mathematics.Providence:American Mathematical Society,1997.
[6]	Batuccelli M, Gibbon J D, Oliver M. Lengths scales in solutions of the complex Ginzburg-Landau equation[J].Physica D,1996,89(3):267-286. doi: 10.1016/0167-2789(95)00275-8
[7]	LI Dong-long,GUO Bo-ling.On Cauchy problem for generalized complex Ginzburg-Landau equation in three dimensions[J].Progress in Natural Science,2003,13(9):658-665. doi: 10.1080/10020070312331344200
[8]	LI Dong-long,DAI Zheng-de.Long time behavior of solution for generalized Ginzburg-Landau equation[J].Math Anal Appl,2007,330(2):934-948. doi: 10.1016/j.jmaa.2006.07.095
[9]	Guo B,Wang X.Finite dimensional behavior for the derivative Ginzburg-Landau equation in two spatial dimensions[J].Physica D,1995,89(1):83-99. doi: 10.1016/0167-2789(95)00216-2
[10]	Crauel H,Flandoli F.Attractors for random dynamical systems[J].Probability Theory and Related Fields,1994,100(3):365-393. doi: 10.1007/BF01193705
[11]	Crauel H,Debussche A,Flandoli F.Random attractors[J].J Dynam Differential Equations,1997,9(2):307-341. doi: 10.1007/BF02219225
[12]	Arnold L.Random Dynamical Systems[M].New York: Springer,1998.
[13]	Prato G Da,Zabezyk J.Stochastic Equations in Infinite Dimensions,Encyclopedia of Mathematics and Its Applications[M].Cambridge: Cambridge University Press,1992.
[14]	Henry D.Geometric Theory of Semilinear Parabolic Equation[M].Berlin: Spring-Verlag,1981.