THE FRACTAL STRUCTURE OF ATTRACTOR FOR THE GENERALIZED KURAMOTO-SIVASHINSKY EQUATIONS

In this paper, the generalized Kuramoto-Sivashinsky equations (GKS) wi th periodic boundary value problem are considered and the construction of inertial sets in space H-2 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 l ocalizing sets of the attractors, these results sharpen and improve th e conclusions of the inertial sets and attractor for GKS equation in [ 1,3,5,7], which describe a kind of geometrical structure of the attrac tors.