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

LI Dong-long; GUO Bo-ling

doi:10.3879/j.issn.1000-0887.2009.08.001

Volume 30 Issue 8

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LI Dong-long, GUO Bo-ling. Asymptotic Behavior of the 2D Generalized Stochastic Ginzburg-Landau Equation With Additive Noise[J]. Applied Mathematics and Mechanics, 2009, 30(8): 883-894. doi: 10.3879/j.issn.1000-0887.2009.08.001

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

doi: 10.3879/j.issn.1000-0887.2009.08.001

LI Dong-long¹,
GUO Bo-ling²

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

Received Date: 2008-02-19
Rev Recd Date: 2009-07-02
Publish Date: 2009-08-15

Abstract

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

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References(14)

References

[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.