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A mathematical model for phase separation: A generalized Cahn–Hilliard equation

✍ Scribed by A. Berti; I. Bochicchio

Publisher
John Wiley and Sons
Year
2011
Tongue
English
Weight
146 KB
Volume
34
Category
Article
ISSN
0170-4214

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✦ Synopsis

In this paper we present a mathematical model to describe the phenomenon of phase separation, which is modelled as space regions where an order parameter changes smoothly. The model proposed, including thermal and mixing effects, is deduced for an incompressible fluid, so the resulting differential system couples a generalized Cahn-Hilliard equation with the Navier-Stokes equation. Its consistency with the second law of thermodynamics in the classical Clausius-Duhem form is finally proved.

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Exponential attractors for the Cahn–Hill
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✍ A. Miranville; S. Zelik 📂 Article 📅 2005 🏛 John Wiley and Sons 🌐 English ⚖ 216 KB

We consider in this article the Cahn-Hilliard equation endowed with dynamic boundary conditions. By interpreting these boundary conditions as a parabolic equation on the boundary and by considering a regularized problem, we obtain, by the Leray-Schauder principle, the existence and uniqueness of sol