弱阻尼KdV方程的惯性分形集<sup>*</sup>

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弱阻尼KdV方程的惯性分形集^*

基金项目: *国家自然科学基金

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

摘要: 本文对非自共轭情形下弱阻尼非线性KdV方程,证明了惯性分形集存在且进行了分形维度的上界估计.
- Kdy方程 /
- 惯性分形 /
- 维度
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

[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).

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