Anomalous scaling for three‐dimensional Cahn‐Hilliard fronts

Abstract

Abstract We prove the stability of the one‐dimensional kink solution of the Cahn‐Hilliard equation under d ‐dimensional perturbations for d ≥ 3. We also establish a novel scaling behavior of the large‐time asymptotics of the solution. The leading asymptotics of the solution is characterized by a length scale proportional to t 1/3 instead of the usual t 1/2 scaling typical to parabolic problems. © 2004 Wiley Periodicals, Inc.