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2007 Global well-posedness for the non-isothermal Cahn-Hilliard equation with dynamic boundary conditions
Ciprian G. Gal
Adv. Differential Equations 12(11): 1241-1274 (2007).

Abstract

We consider a model of non-isothermal phase transition taking place in a confined container. The order parameter $\phi $ is governed by a Cahn--Hilliard-type equation which is coupled with a heat equation for the temperature $\theta $. The former is subject to a nonlinear dynamic boundary condition recently proposed by some physicists to account for interactions with the walls. The latter is endowed with a boundary condition which can be a standard one (Dirichlet, Neumann or Robin) or even dynamic. We thus formulate a class of initial- and boundary-value problems whose local existence and uniqueness is proven by means of the contraction mapping principle. The local solution becomes global owing to suitable a priori estimates.

Citation

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Ciprian G. Gal. "Global well-posedness for the non-isothermal Cahn-Hilliard equation with dynamic boundary conditions." Adv. Differential Equations 12 (11) 1241 - 1274, 2007.

Information

Published: 2007
First available in Project Euclid: 18 December 2012

zbMATH: 1162.35386
MathSciNet: MR2372239

Subjects:
Primary: 35K55
Secondary: 35B30, 35B41, 37L30

Rights: Copyright © 2007 Khayyam Publishing, Inc.

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Vol.12 • No. 11 • 2007
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