The Inertial Fractal Set for Weakly Damped Forced Koreweg-de-Vries Equation

Dai Zheng-de; zhu zhi-we

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Article Navigation > Applied Mathematics and Mechanics > 1995 > 16(1): 33-40

Dai Zheng-de, zhu zhi-we. The Inertial Fractal Set for Weakly Damped Forced Koreweg-de-Vries Equation[J]. Applied Mathematics and Mechanics, 1995, 16(1): 33-40.

Citation:

Dai Zheng-de, zhu zhi-we. The Inertial Fractal Set for Weakly Damped Forced Koreweg-de-Vries Equation[J]. Applied Mathematics and Mechanics, 1995, 16(1): 33-40.

Citation:

Dai Zheng-de, zhu zhi-we. The Inertial Fractal Set for Weakly Damped Forced Koreweg-de-Vries Equation[J]. Applied Mathematics and Mechanics, 1995, 16(1): 33-40.

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The Inertial Fractal Set for Weakly Damped Forced Koreweg-de-Vries Equation

Dai Zheng-de¹,
zhu zhi-we²

1.
Institute of AppIied Mathematics of Yunnan Province;Department of Math., Yunnan Univ., Kunming;
2.
Department of Math., Xijangg Univesity

Received Date: 1994-04-30
Publish Date: 1995-01-15

Abstract

Abstract

In this paper we consider weakly damped forced Kortewegde-Vries equation with non-self-adjoint operator.The existence of inertial fractal set M of this equation is proved,the estimates of the upper bounds of fractal dimension for M are also obtained.
- KdV equation,
- inertial fractal,
- dimension

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References(4)

References

[1]	Ghidaglia,J.M.,Weakly damped forced Korteweg-de-Vries equations behave as a finite dimensional dynamical system in the long time.J.Diff,Equ,74(2)(1988),369-390.
[2]	Constantin,P.,C.Foias and R.Temam,Attractors representing turbulent Flows,Mem.Amer,Math.Soc,314(1985),53.
[3]	Constantin,P.,C.Foias,B.Nicolaenko and R.Temam,Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations,Springer-Verlag(1989).
[4]	Eden,A.,C.Foias,B.Nicolaenko and R.Temam,Inertial sets for dissipative evolution equations,IMA.Preprint.Series,812(1991).