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Fourier spectral approximation to long-time behavior of three dimensional Ginzburg-Landau type equation*

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In this paper, we consider a three dimensional Ginzburg–Landau type equation with a periodic initial value condition. A fully discrete Galerkin–Fourier spectral approximation scheme is constructed, and then the dynamical properties of the discrete system are analyzed. First, the existence and convergence of global attractors of the discrete system are proved by a priori estimates and error estimates of the discrete solution, and the numerical stability and convergence of the discrete scheme are proved. Furthermore, the long-time convergence and stability of the discrete scheme are proved.

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Authors and Affiliations

  1. Department of Mathematics & LMIB, Beihang University, Beijing, 100083, PR China

    Shujuan Lü & Qishao Lu

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  1. Shujuan Lü
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  2. Qishao Lu
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Correspondence to Shujuan Lü.

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Communicated by A. Zhou

*This work was supported by the National Natural Science Foundation of China (No.: 10432010 and 10571010)

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Lü, S., Lu, Q. Fourier spectral approximation to long-time behavior of three dimensional Ginzburg-Landau type equation*. Adv Comput Math 27, 293–318 (2007). https://doi.org/10.1007/s10444-005-9004-x

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  • DOI: https://doi.org/10.1007/s10444-005-9004-x

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