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Volume 16, Issue 3
The Large Time Convergence of Spectral Method for Generalized Kuramoto-Sivashinsky Equation (II)

Xinming Xiang

J. Comp. Math., 16 (1998), pp. 203-212.

Published online: 1998-06

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  • Abstract

In this paper, we study fully discrete spectral method and long time behavior of solution of generalized Kuramoto-Sivashinsky equation with periodic initial condition. We prove that the large time error estimation for fully discrete solution of spectral method. We prove the existence of approximate attractors $\mathcal{A}_N$, $\mathcal{A}_N^k$ respectively and $d (\mathcal{A}_N, \mathcal{A})\to 0$, $d (\mathcal{A}_N^k, \mathcal{A}) \to 0$.  

  • Keywords

Kuramoto-Sivashinsky equation, large time convergence, Approximate attractor, Upper semicontinuity of attractors.

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COPYRIGHT: © Global Science Press

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@Article{JCM-16-203, author = {Xiang , Xinming}, title = {The Large Time Convergence of Spectral Method for Generalized Kuramoto-Sivashinsky Equation (II)}, journal = {Journal of Computational Mathematics}, year = {1998}, volume = {16}, number = {3}, pages = {203--212}, abstract = {

In this paper, we study fully discrete spectral method and long time behavior of solution of generalized Kuramoto-Sivashinsky equation with periodic initial condition. We prove that the large time error estimation for fully discrete solution of spectral method. We prove the existence of approximate attractors $\mathcal{A}_N$, $\mathcal{A}_N^k$ respectively and $d (\mathcal{A}_N, \mathcal{A})\to 0$, $d (\mathcal{A}_N^k, \mathcal{A}) \to 0$.  

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9153.html} }
TY - JOUR T1 - The Large Time Convergence of Spectral Method for Generalized Kuramoto-Sivashinsky Equation (II) AU - Xiang , Xinming JO - Journal of Computational Mathematics VL - 3 SP - 203 EP - 212 PY - 1998 DA - 1998/06 SN - 16 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9153.html KW - Kuramoto-Sivashinsky equation, large time convergence, Approximate attractor, Upper semicontinuity of attractors. AB -

In this paper, we study fully discrete spectral method and long time behavior of solution of generalized Kuramoto-Sivashinsky equation with periodic initial condition. We prove that the large time error estimation for fully discrete solution of spectral method. We prove the existence of approximate attractors $\mathcal{A}_N$, $\mathcal{A}_N^k$ respectively and $d (\mathcal{A}_N, \mathcal{A})\to 0$, $d (\mathcal{A}_N^k, \mathcal{A}) \to 0$.  

Xinming Xiang. (1970). The Large Time Convergence of Spectral Method for Generalized Kuramoto-Sivashinsky Equation (II). Journal of Computational Mathematics. 16 (3). 203-212. doi:
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