LOCALIZATION AND APPROXIMATION OF ATTRACTORS FOR THE KURAMOTO-SIVASHINSKY EQUATIONS

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