The Convergence of Attractors for Some Discrete Cahn-Hilliard Systems

Abstract

In this article, we use a finite difference scheme to discretize the Cahn-Hilliard equation with the space step size . We first prove that this semidiscrete system inherits two important properties, called the conservation of mass and the decrease of the total energy, from the original equation. Then, we show that the semidiscrete system has an attractor on a subspace of . Finally, the convergence of attractors is established as the space step size of the semidiscrete Cahn-Hilliard equation tends to 0.