Abstract
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 H2 is given. Furthermore, 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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Guo Boling,Progress in Natural Science,3, 4 (1993), 327–340.
Gao Boling,J. Math. Res. & Expo.,11, 1 (1991), 57–65.
P. Constantin, C. Foias and R. Temam.,Mem. Amer. Math. Soc., N314 (1985).
P. Constantin, C. Foias, B. Nicolaenko and R. Temam, IntegralManifolds and Inertial Manifolds for Dissipative Partial Differential Equations, Springer-Verlag (1989).
A. Eden, C. Foias, B. Nicolaenko and R. Temam, Inertial sets for dissipative evolution equations,IMA, Preprint Series 812 (1991).
A. V. Babin and M. I. Vishik,J. Math. Pures Appl.,62 (1983), 441–491.
C. Foias and R. Temam,Physics D,32 (1988), 163–182.
K. Promislow and R. Temam,J. Dynam. Diff. Eq.,3 (1991), 491–514.
Dai Zhengde, Guo Boling and Gou Hongjun,J. Part. Diff. Eq.,8, 1 (1995), 37–81.
Author information
Authors and Affiliations
Additional information
Communicated by Zhang Hongqin
Project supported by the National Natural Science Foundation of China and Applied Research Foundation of Yunnan Province.
Rights and permissions
About this article
Cite this article
Zhengde, D., Boling, G. & Guoguang, L. The fractal structure of attractor for the generalized Kuramoto-Sivashinsky equations. Appl Math Mech 19, 263–277 (1998). https://doi.org/10.1007/BF02453391
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02453391