广义Kuramoto-Sivashinsky方程吸引子的分形结构<sup>*</sup>

广义Kuramoto-Sivashinsky方程吸引子的分形结构^*

基金项目: * 国家自然科学基金资助;云南省基金资助

摘要: 首先给出广义Kuramoto-Sivashinsky(GKS)方程周期初边值问题在H²空间惯性集的构造,进而给出并证明GKS方程吸引子的分形结构,同时发现吸引子的一个分形局部化指数型逼近序列.上述结果精细和推进了[1,3,5,7]关于惯性集和吸引子的结论,刻划了吸引子的一种几何结构.
- 广义KS方程 /
- 吸引子 /
- 惯性集 /
- 分形
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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