| Abstract: | The aim of this paper is to provide explicitly a sequence of m-dimensional approximate inertial manifolds M,j,j = 1,2,...,for each positive integer m,for the Kuramoto-Sivashinsky equations.A very thin neighborhood into which the orbits enter with an exponential speed and in a finite time is associated with each manifold.The thickness of these neighborhoods decreases with increasing m for a fixed order j.Besides,the neighborhoods localize the global attractor and aid in the approximate computation of large-time solutions of the Kuramoto-Sivashinsky equations. |
