| 广义Fitz－Hugh－Nagumo方程组的整体吸引子及惯性流形 |
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| 引用本文： | 吴永辉,王明新. 广义Fitz－Hugh－Nagumo方程组的整体吸引子及惯性流形[J]. 应用数学学报, 1996, 0(2) |
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| 作者姓名： | 吴永辉 王明新 |
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| 作者单位： | 中国科学院大气物理所，东南大学数学力学系 |
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| 摘 要： | 本文考虑广义Ｆｉｔｚ－Ｈｕｇｈ－Ｎａｇｕｍｏ方程组的初边值问题．去掉解属于某不变区域的限制，我们证明了初值属于Ｌ２情形下整体吸引子的存在性，并给出其维数估计．对二维情形证明了其惯性流形的存在性．我们的方法简化了Ｐ．Ｃｏｎｓｔａｎｔｉｎ等人的工作．
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| 关 键 词： | 整体吸引子，Hausdorff及Fractal维数，惯性流形 |
GLOBAL ATTRACTOR OF THE GENERALIZED FITZ-HUGH-NAGUMO EQUATIONS AND ITS INERTIAL MANIFOLD |
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| WU YONGHUI. GLOBAL ATTRACTOR OF THE GENERALIZED FITZ-HUGH-NAGUMO EQUATIONS AND ITS INERTIAL MANIFOLD[J]. Acta Mathematicae Applicatae Sinica, 1996, 0(2) |
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| Authors: | WU YONGHUI |
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| Abstract: | This paper deals with the initial boundary value problem of the generalizedFitz-Hugh-Nagumo equations.Without the restriction that the initial data contain in someinvariat set,we prove the existence of global attractor of the above system in l,and giveupper botmds of the attractor.Moreover, we construct the inertial manifold for the abovesystem as the space dimension is less than or equal to 2.Our approach simperes the workof P.Constantin,C.Foias,B.Nicolaenko,and R.Temam. |
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| Keywords: | Global attractor Hausdorff dimension and fractal dimension inertial manifolds |
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