Anomalous scaling for three‐dimensional Cahn‐Hilliard fronts | Zendy

Korvola Timo | Zendy; Kupiainen Antti | Zendy; Taskinen Jari | Zendy

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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.

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