Global asymptotic limit of solutions of the cahn-hilliard equation

Abstract

We study the asymptotic limit, as ε ↘ 0, of solutions of the Cahn–Hilliard equation utε = Δ(−εΔuε + ε-1f(uε)) under the assumption that the initial energy ∫Ω[ε/1|∇uε(.,0)|2+1/εF(uε(.,0))]is bounded independent of ε. Here f = F’, and F is a smooth function taking its global minimum 0 only at u = ±1. We show that there is a subsequence of (uε)0 0, regardless of initial energy distributions. © 1996 J. differential geometry.