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Stability of Cahn-Hilliard fronts

✍ Scribed by Jean Bricmont; Antti Kupiainen; Jari Taskinen

Book ID
101241361
Publisher
John Wiley and Sons
Year
1999
Tongue
English
Weight
473 KB
Volume
52
Category
Article
ISSN
0010-3640

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✦ Synopsis

We prove stability of the kink solution of the Cahn-Hilliard equation ∂tu

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

The proof is based on an inductive renormalization group method, and we obtain detailed asymptotics of the solution as t → ∞.

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Asymptotic behavior near planar transiti
Asymptotic behavior near planar transition fronts for the Cahn–Hilliard equation
✍ Peter Howard 📂 Article 📅 2007 🏛 Elsevier Science 🌐 English ⚖ 803 KB

We consider the asymptotic behavior of perturbations of planar wave solutions arising in the Cahn-Hilliard equation in space dimensions d ≥ 2. Such equations are well known to arise in the study of spinodal decomposition, a phenomenon in which rapid cooling of a homogeneously mixed binary alloy caus