The Fractal Structure of Attractor for the Generalized Kuramoto-Sivashinsky Equations
-
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.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.
-
Key words:
- GKS equation /
- attractor /
- inertial set /
- fractal structure
-
[1] Guo Boling,The global attractors for the periodic initial value problem of generalized Kuramoto-Sivashinsky type equations,Progress in Natural Science,3(4)(1993),327-340. [2] Gao Boling,The existence and none xistence of a global smooth solution for the initial value problem of gener alized Kuramoto-Sivashinsky type equations,J.Math.Res.&Expo,11(1),1991,57-65. [3] P.Constantin,C.Foias and R.Temam,Mem.Amer.Math.Soc.,N314(1985). [4] P.Constantin,C.Foias,B.Nicolaenko and R.Temam,Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations Springer-Verlag(1989). [5] A.Eden,C.Foias,B.Nicolaenko and R.Temam,Inertial sets for dissipative evolution equations,IMA.Preprint Series 812(1991). [6] A.V.Babin and M.I.Vishik,Regular attractors of semigroups and evolution equations,J.Math.Pures Appl.,62(3)(1983),441-491. [7] C.Foias and R.Temam,The algebra approximation of attractors,the finite dime nsional case,Physics D,32(1988),163-182. [8] K.Promislom and R.Temam,Localization and approximation of attractors for the Ging burg-Landaw equation,J.Dynam.Diff.Eq.,3(4)(1991),491-514. [9] Dai Zheng de,Guo Boling and Gou Hong jun,The inertial fractal sets for no nlinear schroding erequations,J.Part.Diff.Eq.,8(1)(1995),37-81.
点击查看大图
计量
- 文章访问数: 1778
- HTML全文浏览量: 56
- PDF下载量: 543
- 被引次数: 0