Asymptotic behavior of a Cahn-Hilliard equation with Wentzell boundary conditions and mass conservation

Ciprian G. Gal; Hao Wu

doi:10.3934/dcds.2008.22.1041

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2008, Volume 22, Issue 4: 1041-1063. Doi: 10.3934/dcds.2008.22.1041

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Asymptotic behavior of a Cahn-Hilliard equation with Wentzell boundary conditions and mass conservation

Ciprian G. Gal^1, and
Hao Wu^2,

1.
Department of Mathematics, University of Missouri, Columbia, MO 65211
2.
School of Mathematical Sciences, Fudan University, Han Dan Road 220, 200433 Shanghai

Received: May 31, 2007

Revised: November 30, 2007

Published: September 2008

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Abstract

In this article, we consider a Cahn-Hilliard model with boundary conditions of Wentzell type and mass conservation. We show that each solution of this problem converges to a steady state as time goes to infinity, provided that the potential function $f$ is real analytic and satisfies certain growth assumptions. Estimates of the rate of convergence to equilibrium are obtained as well. We also recall some results about the existence of global and exponential attractors and their properties.

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Mathematics Subject Classification: Primary: 35K55, 35B40; Secondary: 74N20.

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