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Asymptotic attractors of KdV–KSV equations

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Abstract

In this paper, we apply the method of orthogonal decomposition to prove the existence of asymptotic attractors for the KdV–KSV equations. Moreover, the dimensions estimate of asymptotic attractors is obtained.

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References

  1. Chow, S.N., Lu, K.: Inertial manifolds for flows in Banach spaces. J. Differ. Equ. 74(1), 285–317 (1988)

    Article  Google Scholar 

  2. Christor, C.I., Velarde, M.G.: Diddipative solitions. Physica D 86(1–2), 323–347 (1995)

    Article  MathSciNet  Google Scholar 

  3. Foias, C., Sell, G., Temam, R.: Inertial manifolds for nonlinear evolutionary equations. J. Differ. Equ. 73(2), 309–353 (1988)

    Article  MathSciNet  Google Scholar 

  4. Gao, P., Zhao, Y.: Global attactor for damped KdV-KSV equation in an unbounded domain. Acta Scientiarum Naturalium Universitatis Pekinensis 41(1), 5–8 (2002). (in Chinese)

    MATH  Google Scholar 

  5. Robinson, J.C.: Infinite-Dimensional Dynamical Systems. Cambridge University Press, Cambridge (2001)

    Book  Google Scholar 

  6. Ruggieri, M.P., Speciale, M.: Quasi self-adjoint coupled KdV-like equations. AIP Conf. Proc. 1558, 1220–1223 (2013)

    Article  Google Scholar 

  7. Ruggieri, M.P., Speciale, M.: New exact solutions for a coupled KdV-like model. J. Phys. Conf. Ser. 482, 012036 (2014)

    Article  Google Scholar 

  8. Ruggieri, M.P., Speciale, M.P.: Conservation laws for a model derived from two layer-fluids. J. Phys. Conf. Ser. 482, 012037 (2014)

    Article  Google Scholar 

  9. Temam, R.: Infinite-Dimensional Dynamical Systems in Mechanics and Physics. Springer, New York (1997)

    Book  Google Scholar 

  10. Wang, G.X., Liu, Z.R.: The asymptotic attractors of Kuramoto-Sivashinsky equation. Acta Math. Appl. Sin. 23(3), 329–336 (2000). (in Chinese)

    MathSciNet  MATH  Google Scholar 

  11. Xia, H.Q.: Initial-boundary value problems for the KdV-KSV equation. Math. Appl. 11(2), 116–121 (1998). (in Chinese)

    MathSciNet  MATH  Google Scholar 

  12. Xia, H.Q.: Global attactor for a damped KdV-KSV equation. Math. Appl. 12(1), 31–36 (1999). (in Chinese)

    MathSciNet  MATH  Google Scholar 

  13. Zhu, C.S.: Asymptotic attractors of Benjamin-Bona-Mahony equations. Eur. J. Pure. Appl. Math. 1(2), 3–10 (2008)

    MathSciNet  MATH  Google Scholar 

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Acknowledgements

The author would like to thank the anonymous referee for his/her valuable suggestions and comments to improve the quality of the paper.

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Correspondence to Qiangheng Zhang.

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Zhang, Q. Asymptotic attractors of KdV–KSV equations. SeMA 75, 535–544 (2018). https://doi.org/10.1007/s40324-018-0149-1

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  • DOI: https://doi.org/10.1007/s40324-018-0149-1

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