The Fractal Structure of Attractor for the Generalized Kuramoto-Sivashinsky Equations

Dao Zhengde; Guo Boling; Lin Guoguang

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Article Navigation > Applied Mathematics and Mechanics > 1998 > 19(3): 243-256

Dao Zhengde, Guo Boling, Lin Guoguang. The Fractal Structure of Attractor for the Generalized Kuramoto-Sivashinsky Equations[J]. Applied Mathematics and Mechanics, 1998, 19(3): 243-256.

Citation:

Dao Zhengde, Guo Boling, Lin Guoguang. The Fractal Structure of Attractor for the Generalized Kuramoto-Sivashinsky Equations[J]. Applied Mathematics and Mechanics, 1998, 19(3): 243-256.

Citation:

Dao Zhengde, Guo Boling, Lin Guoguang. The Fractal Structure of Attractor for the Generalized Kuramoto-Sivashinsky Equations[J]. Applied Mathematics and Mechanics, 1998, 19(3): 243-256.

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The Fractal Structure of Attractor for the Generalized Kuramoto-Sivashinsky Equations

1.
Department to Mathematics, Yunnan University, Kunming 650091, P. R. China;
2.
P. O. Box 8009, Beijing 100088, P. R. China;
3.
Department of Mathematics, Yunnan University, Kunming 650091, P. R. China

Received Date: 1996-07-07
Rev Recd Date: 1997-09-10
Publish Date: 1998-03-15

Abstract

Abstract

In this paper,the g eneralized Kuramoto-Sivashinsky e quations(GKS)with periodic initial boundar y value pr oblem are consider ed and the constr uction o f ine rtial sets in space H² is given. Furthemore,this paper gives and proves the fractal structure of attractors for GKS equations,and find out an exponentially approxim ating sequence of compact fractal localizing sets of the attractors, the sere sults sharpen and improve the conclusions of the inertial sets and attractor for GKS equation in[1,3,5,7],which describe a kind of geometrical structure of the attractors.
- GKS equation,
- attractor,
- inertial set,
- fractal structure

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References(9)

References

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