Global asymptotic limit of solutions of the Cahn-Hilliard equation

Abstract

We study the asymptotic limit, as \ 0, of solutions of the Cahn-Hilliard equation 1 under the assumption that the initial energy is bounded independent of . Here / = F', and F is a smooth function taking its global minimum 0 only at u -1. We show that there is a subsequence of {t e }o<e<i converging to a weak solution of an appropriately defined limit Cahn-Hilliard problem. We also show that, in the case of radial symmetry, all the interfaces of the limit have multiplicity one for almost all time t > 0, regardless of initial energy distributions.