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Asymptotic behavior of 2D generalized stochastic Ginzburg-Landau equation with additive noise

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Abstract

The 2D generalized stochastic Ginzburg-Landau equation with additive noise is considered. The compactness of the random dynamical system is established with a priori estimate method, showing that the random dynamical system possesses a random attractor in H 10 .

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References

  1. Doering, C. R., Gibbon, J. D., Holm, D. D., and Nicolaenko, B. Low-dimensional behavior in the complex Ginzburg-Landau equation. Nonlinearity 1, 279–309 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  2. Ghidaglia, J. M. and Héron, B. Dimension of the attractor associated to the Ginzburg-Landau equation. Physica D 28(3), 282–304 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  3. Bartuccelli, M., Constantin, P., Doering, C. R., Gibbon, J. D., and Gisselfält, M. On the possibility of soft and hard turbulence in the complex Ginzburg-Landau equation. Physica D 44(3), 421–444 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  4. Doering, C. R., Gibbon, J. D., and Levermore, C. D. Weak and strong solutions of the complex Ginzburg-Landau equation. Physica D 71(3), 285–318 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  5. Levermore, C. D. and Oliver, M. The complex Ginzburg-Landau equation as a model problem. Dynamical Systems and Probabilistic Methods in Partial Differential Equations, Lectures in Applied Mathematics (eds. Deift, P., Levermore, C. D., and Wayne, C. E.), Vol. 31, American Mathematical Society, Providence (1996)

    Google Scholar 

  6. Batuccelli, M., Gibbon, J. D., and Oliver, M. Lengths scales in solutions of the complex Ginzburg-Landau equation. Physica D 89(3), 267–286 (1996)

    Article  MathSciNet  Google Scholar 

  7. Li, Donglong and Guo, Boling. On Cauchy problem for generalized complex Ginzburg-Landaue quation in three dimensions. Progress in Natural Science 13(9), 658–665 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  8. Li, Donglong and Dai, Zhengde. Long time behavior of solution for generalized Ginzburg-Landau equation. Journal of Mathematics Analysis and Applications 330(2), 934–948 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  9. Guo, B. and Wang, X. Finite dimensional behavior for the derivative Ginzburg-Landau equation in two spatial dimensions. Physica D 89(1), 83–99 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  10. Crauel, H. and Flandoli, F. Attractors for random dynamical systems. Probab. Theory Relat. Fields 100, 365–393 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  11. Crauel, H., Debussche, A., and Flandoli, F. Random attractors. Journal of Dynamics and Differential Equations 9(2), 307–341 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  12. Arnold, L. Random Dynamical Systems, Springer-Verlag, New York (1998)

    MATH  Google Scholar 

  13. Prato, G. Da and Zabezyk, J. Stochastic Equations in Infinite Dimensions, Encyclopedia of Mathematics and its Applications, Cambridge University Press, Cambridge (1992)

    Google Scholar 

  14. Henry, D. Geometric Theory of Semilinear Parabolic Equation, Springer-Verlag, Berlin (1981)

    Google Scholar 

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Authors and Affiliations

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

    Dong-long Li  (李栋龙)

  2. Institute of Applied Physics and Computational Mathematics, Beijing, 100088, P. R. China

    Bo-ling Guo  (郭柏灵)

Authors
  1. Dong-long Li  (李栋龙)
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  2. Bo-ling Guo  (郭柏灵)
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Correspondence to Dong-long Li  (李栋龙).

Additional information

Contributed by Bo-ling GUO

Project supported by the National Natural Science Foundation of China (No. 10661002), the Natural Science Foundation of Guangxi (No. 0832065), and the Excellent Talents Fund of Guangxi (No. 0825)

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Li, Dl., Guo, Bl. Asymptotic behavior of 2D generalized stochastic Ginzburg-Landau equation with additive noise. Appl. Math. Mech.-Engl. Ed. 30, 945–956 (2009). https://doi.org/10.1007/s10483-009-0801-x

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  • DOI: https://doi.org/10.1007/s10483-009-0801-x

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