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Attractor for lattice system of dissipative Zakharov equation

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Abstract

We consider the asymptotic behavior of solutions of an infinite lattice dynamical system of dissipative Zakharov equation. By introducing new weight inner product and norm in the space and establishing uniform estimate on “Tail End” of solutions, we overcome some difficulties caused by the lack of Sobolev compact embedding under infinite lattice system, and prove the existence of the global attractor; then by using element decomposition and the covering property of a polyhedron in the finite-dimensional space, we obtain an upper bound for the Kolmogorov ɛ-entropy of the global attractor; finally, we present the upper semicontinuity of the global attractor.

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Authors and Affiliations

  1. School of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411105, P. R. China

    Fu Qi Yin & Cui Hui Xiao

  2. Mathematics and Science College of Shanghai Normal University, Shanghai, 200234, P. R. China

    Sheng Fan Zhou

  3. School of Mathematics and Physics of University of South China, Hengyang, 421001, P. R. China

    Zi Gen Ouyang

Authors
  1. Fu Qi Yin
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  2. Sheng Fan Zhou
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  3. Zi Gen Ouyang
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  4. Cui Hui Xiao
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Corresponding author

Correspondence to Cui Hui Xiao.

Additional information

This research is supported by National Natural Science Foundation of People’s Republic of China (10771139); Partly supported by A Project Supported by Scientific Research Fund of Hu’nan Provincial Education on Department(08A070; 08A071)

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Yin, F.Q., Zhou, S.F., Ouyang, Z.G. et al. Attractor for lattice system of dissipative Zakharov equation. Acta. Math. Sin.-English Ser. 25, 321–342 (2009). https://doi.org/10.1007/s10114-008-5595-8

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  • DOI: https://doi.org/10.1007/s10114-008-5595-8

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