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Anomalous scaling for three‐dimensional Cahn‐Hilliard fronts
Author(s) -
Korvola Timo,
Kupiainen Antti,
Taskinen Jari
Publication year - 2005
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.20055
Subject(s) - scaling , cahn–hilliard equation , mathematics , stability (learning theory) , scale (ratio) , mathematical analysis , statistical physics , geometry , partial differential equation , physics , computer science , quantum mechanics , machine learning
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.