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Stability of Cahn‐Hilliard fronts
Author(s) -
Bricmont Jean,
Kupiainen Antti,
Taskinen Jari
Publication year - 1999
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/(sici)1097-0312(199907)52:7<839::aid-cpa4>3.0.co;2-i
Subject(s) - mathematics , cahn–hilliard equation , stability (learning theory) , renormalization , renormalization group , mathematical analysis , mathematical physics , differential equation , machine learning , computer science
We prove stability of the kink solution of the Cahn‐Hilliard equation ∂ t u = ∂ 2 x ( ∂ 2 xu − u /2 + u 3 /2), x ∈ ℝ. The proof is based on an inductive renormalization group method, and we obtain detailed asymptotics of the solution as t → ∞. We prove stability of the kink solution of the Cahn‐Hilliard equation ∂ t u = ∂ 2 x ( ∂ 2 xu − u /2 + u 3 /2), x ∈ ℝ. The proof is based on an inductive renormalization group method, and we obtain detailed asymptotics of the solution as t → ∞. © 1999 John Wiley & Sons, Inc.