This book develops the theory of global attractors for a class of parabolic PDEs that includes
reaction-diffusion equations and the Navier-Stokes equations, two examples that are treated …

We evaluate several alternative methods for the approximation of inertial manifolds for the
one-dimensional Kuramoto-Sivashinsky equation (KSE). A method motivated by the …

The authors present a connection between the concepts of determining nodes and inertial
manifolds with that of finite difference and finite volumes approximations to dissipative partial …

We consider the 2D Navier-Stokes equations on a square with periodic boundary
conditions. Dividing the square into N equal subsquares, we show that if the asymptotic …

§ 1. Introduction. The theory of invariant manifolds plays an important role in the study of
dynamics of nonlinear systems in finite dimensional or infinite dimensional spaces. Such …

In contrast with the existing theories of inertial manifolds, which are based on the self-adjoint
assumption of the principal differential operator, in this paper we show that for general …

The problem of computing a smooth invariant manifold for a finite-dimensional dynamical
system is considered. In this paper, it is assumed that the manifold can be parameterized …

The present monograph is dedicated to a new branch of the theory of climate, which is titled
by the authors," Mathematical Theory of Climate." The foundation of this branch is the …

A closure model for turbulent flows is developed based on a dynamical system theory. An
appropriately discretized formulation of the governing equations is considered for this …

In this article we survey some recent results concerning attractors, inertial manifolds and
approximate inertial manifolds for dissipative evolution equations and in particular for the …