| THE LARGE TIME CONVERGENCE OF SPECTRAL METHOD FOR GENERALIZED KURAMOTO-SIVASHINSKY EQUATION (Ⅱ) |
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| 作者姓名： | Xin-ming Xiang |
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| 作者单位： | Shanghai Normal University，Shanghai 200234，China |
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| 基金项目： | Supported by the National Fund of Natueal Sciences and by Science and Technology Fund of
Shanghai Higher Education |
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| 摘 要： | 1.IntroductionInthepaper1],westudedthegeneralizedKuramotrySivashinskyequationWeProvedtheexistenceanduniquenessofglobalsolutionforperiodicinitialproblemandgavethelargetimeerrorestimationforthesolutionofcontinuousspectralmethod.Theaimofthispaperistostudyfullydiscretespectralmethodandthelongtimebehaviorofthesolutionofthissystem.In61wegiventhelargetimeerrorestimationforfullydiscretesolutionofspectralmethod.In52weprove-theexistenceofapproximateattractorsAN,4anding3weprovetheconvergenceofapproal…
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The Large Time Convergence of Spectral Method for Generalized Kuramoto-Sivashinsky Equation (II) |
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| Xin-ming Xiang.The Large Time Convergence of Spectral Method for Generalized Kuramoto-Sivashinsky Equation (II)[J].Journal of Computational Mathematics,1998,16(3):203-212. |
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| Authors: | Xin-ming Xiang |
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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 $d (\mathcal{A}_N, \mathcal{A})\to 0$, $d (\mathcal{A}_N^k, \mathcal{A}) \to 0$. |
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| Keywords: | Kuramoto- Sivashinsky equation large time convergence Approximate attractor Upper semicontinuity of attractors |
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