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Finite dimension of global attractors for dissipative equations governing modulated wave

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Abstract

The finite dimension of the global attractors for the systems of the perturbed and unperturbed dissipative Hamiltonian amplitude equations governing modulated wave are investigated. An interesting result is also obtained that the upper bound of the dimension of the global attractor for the perturbed equation is independent of ε.

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References

  1. Guo Boling, Dai Zhengde, Attractor for the dissipative Hamiltonian amplitude equation governing modulated wave instabilities, Discrete and Continuous Dynamical Systems, 1998, 4(4): 783–793.

    Article  MATH  MathSciNet  Google Scholar 

  2. Dai Zhengde, Yang Lin, Attractor for the unperturbed dissipative Hamiltonian amplitude wave. (to appear)

  3. Ghidaglia, J.M., Finite dimensional behavior for weakly damped driven Schrödinger equations, Anal. Nonlinearie, 1988, 5(4): 365–405.

    MATH  MathSciNet  Google Scholar 

  4. Li Yongsheng, Cheng Qingyi, Finite dimensional global attractor for dissipative Schrödinger-Boussinesq equations, J. Math. Anal. Appl., 1997, 205: 107–132.

    Article  MATH  MathSciNet  Google Scholar 

  5. Ghidaglia, J. M., Weakly damped forced KdV equations behave as a finite dimensional dynamical system in the long time, J Differential Equations, 1988, 74: 369–390.

    Article  MATH  MathSciNet  Google Scholar 

  6. Temam, R., Infinite Dynamical System in Mechanics and Physics, Berlin: Springer-Verlag, 1988.

    Google Scholar 

  7. Ghidaglia, J. M., Temam, R., Attractors for damped nonlinear hyperbolic equations, J. Math. Pures Appl., 1987, 66: 273–319.

    MATH  MathSciNet  Google Scholar 

  8. Dai Zhengde, Regularity of the attractor for the dissipative Hamiltonian amplitude equation governing modulated wave instabilities, Acta Math. Appl. Sinica, 2002, 18(B)(2): 263–272.

    Article  MATH  Google Scholar 

  9. Dai Zhengde, Guo Boling, Global attractor of nonlinear strain waves in elastic waveguides, Acta. Math. Sci., 2000, 20B(3): 322–334.

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Dept. of Appl. Math., Shanghai Jiaotong Univ., 200240, Shanghai, China

    Yang Lin & Dai Zhengde

  2. Dept. of Math., Yunnan Univ., 650091, Kunming, China

    Yang Lin & Dai Zhengde

Authors
  1. Yang Lin
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  2. Dai Zhengde
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Additional information

Supported Partially by the National Natural Science Foundation of China (10131050), the Education Ministry of China and Shanghai Science and Technology Committee (03QMH1407).

Supported by the National Natural Science Foundation of China (19861004).

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Lin, Y., Zhengde, D. Finite dimension of global attractors for dissipative equations governing modulated wave. Appl. Math. Chin. Univ. 18, 421–430 (2003). https://doi.org/10.1007/s11766-003-0069-3

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  • DOI: https://doi.org/10.1007/s11766-003-0069-3

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