Metastable Patterns for the Cahn-Hilliard Equation, Part I

In this paper we study the dynamics of the one-dimensional Cahn-Hilliard equation in a neighborhood of an equilibrium having N + 1 transition layers. An approximation for an N-dimensional invariant manifold and "slow channel" are defined, and it is proved that ff a solution of the Cahn-Hilliard equation starts outside but close to the slow channel around the approximate manifold, then it will approach the channel at an exponentially large speed. After it enters the slow channel, it will follow the approximate manifold with speed O(e−c/ε) and stay in the channel for exponentially large time.