广义Kuramoto-Sivashinsky方程吸引子的分形结构  

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

作　　者：戴正德[1] 郭柏灵[1] 林国广[1] 

机构地区：[1]云南大学数学系

出　　处：《应用数学和力学》1998年第3期243-256,共14页Applied Mathematics and Mechanics

基　　金：国家自然科学基金;云南省基金

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。In this paper, the generalized Kuramoto_Sivashinsky equations (GKS) with periodic initial boundary value problem are considered and the construction of inertial sets in space H 2 is given. Furthemore, this paper gives and proves the fractal structure of attractors for GKS equations, and find out an exponentially approximating sequence of compact fractal localizing sets of the attractors, these results 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.

关 键 词：广义 吸引子 分形 K-S方程 初边值问题 

分 类 号：O175.26[理学—数学]