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Dec 2003 THE CAHN-HILLIARD'S EQUATION WITH BOUNDARY NONLINEARITY AND HIGH VISCOSITY
ROBERT WILLIE
Methods Appl. Anal. 10(4): 589-602 (Dec 2003).

Abstract

The paper studies in less general scales of Banach spaces the dynamics generated by a Cahn-Hilliard type equation in a smooth open bounded domain of any space dimensions. The equation on the boundary satisfy nonlinear conditions. It establishes local well posedness of the problem and a priori uniform on the domain boundedness and existence in the large of the solutions is studied. It also discusses the asymptotic behaviour of the solutions in the form of existence of a global attractor. An adequate notion of upper semicontinuity of the attractor in the limit of high viscosity is considered and the limit attractor is found to correspond to finite dimensional processes. These processes are depicted by limits of the spatial average solutions of the problem.

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ROBERT WILLIE. "THE CAHN-HILLIARD'S EQUATION WITH BOUNDARY NONLINEARITY AND HIGH VISCOSITY." Methods Appl. Anal. 10 (4) 589 - 602, Dec 2003.

Information

Published: Dec 2003
First available in Project Euclid: 20 August 2004

zbMATH: 1078.35059
MathSciNet: MR2105041

Rights: Copyright © 2003 International Press of Boston

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Vol.10 • No. 4 • Dec 2003
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