| 带五次项的NLS方程及其谱逼近的整体吸引子的维数估计 |
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| 引用本文： | 向新民,顾绍泉.带五次项的NLS方程及其谱逼近的整体吸引子的维数估计[J].应用数学学报,2003,26(4):664-674. |
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| 作者姓名： | 向新民 顾绍泉 |
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| 作者单位： | 上海师范大学数理信息学院,上海,200234 |
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| 基金项目： | 国家自然料学基金(19871056号)，上海科技发展基金，上海市高校科技发展基金(03DZ21号) |
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| 摘 要： | 通过给出一般发展方程和其近似方程解的整体吸引子的Hausdorff维数上界间的关系，继1，2]的讨论，本文进一步得到了带五次项的NLS方程和半离散Fourier谱近似解的整体吸引子的Hausdorff维数的上界估计。
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| 关 键 词： | NLS方程 谱逼近 整体吸引子 维数估计 无限维动力系统 |
THE HAUSDORFF DIMENSIONS ESTIMATE FOR THE GLOBAL ATTRACTORS OF THE NLS EQUATION WITH QUINTIC TERMS AND THE SPECTRAL APPROXIMATION |
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| XIANG XINMIN GU SHAOQUAN.THE HAUSDORFF DIMENSIONS ESTIMATE FOR THE GLOBAL ATTRACTORS OF THE NLS EQUATION WITH QUINTIC TERMS AND THE SPECTRAL APPROXIMATION[J].Acta Mathematicae Applicatae Sinica,2003,26(4):664-674. |
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| Authors: | XIANG XINMIN GU SHAOQUAN |
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| Abstract: | In this paper we first give the relation between the Hausdorff dimensions for the global attractors of the general evolution equation and the approximate solution. Then we get the upper bounds of the Hausdorff dimensions for the global attractors of the NLS equation with Quintic Terms and the semi-discrete Fourier Spectral solution after the results in paper 1,2]. |
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| Keywords: | Global attractor NLS equation semi-discrete Spectral scheme Hausdorff dimension |
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