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Applied Mathematics and Mechanics (English Edition) ›› 1998, Vol. 19 ›› Issue (3): 263-277.

• 论文 • 上一篇    下一篇

THE FRACTAL STRUCTURE OF ATTRACTOR FOR THE GENERALIZEDKURAMOTO-SIVASHINSKY EQUATIONS

戴正德1, 郭柏灵2, 林国广1   

  1. 1. Department to Mathematics, Yunnan University, Kunming 650091. P. R. China;
    2. P. O. Box 8009, Beijing 100088, P/ R. China
  • 收稿日期:1996-07-07 修回日期:1997-09-10 出版日期:1998-03-18 发布日期:1998-03-18
  • 基金资助:
    Project suppoeted by the National Natural Science Foundation of China and Applied Researeh Foundation of Yunnan Province

THE FRACTAL STRUCTURE OF ATTRACTOR FOR THE GENERALIZED KURAMOTO-SIVASHINSKY EQUATIONS

Dai Zhengde1, Guo Boling2, Lin Guoguang1   

  1. 1. Department to Mathematics, Yunnan University, Kunming 650091. P. R. China;
    2. P. O. Box 8009, Beijing 100088, P/ R. China
  • Received:1996-07-07 Revised:1997-09-10 Online:1998-03-18 Published:1998-03-18
  • Supported by:
    Project suppoeted by the National Natural Science Foundation of China and Applied Researeh Foundation of Yunnan Province

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摘要： In this paper, the generalized Kuramoto-Sivashinsky equations (GKS)withperiodic initial boundary value problem are considered and the construction of inertialsets in space H2 is given. Furthermore this paper gives and find out an exponentially approximating of attractors for GKS equations and find out an exponentially approximatingsequence of compact fractal localizing sets of the attractors, these results sharpen and improve the conclusions of the conclusions of the inertial sets and attractor.for GKS equation in [l, 3, 5, 7]. which describe a kind of geometrical structure of the attractors.

关键词: GKS equation, attractor, inertial set, fractal structure

Abstract: In this paper, the generalized Kuramoto-Sivashinsky equations (GKS)withperiodic initial boundary value problem are considered and the construction of inertialsets in space H2 is given. Furthermore this paper gives and find out an exponentially approximating of attractors for GKS equations and find out an exponentially approximatingsequence of compact fractal localizing sets of the attractors, these results sharpen and improve the conclusions of the conclusions of the inertial sets and attractor.for GKS equation in [l, 3, 5,7]. which describe a kind of geometrical structure of the attractors.

Key words: GKS equation, attractor, inertial set, fractal structure

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