American Institute of Mathematical Sciences

December  2008, 22(4): 1041-1063. doi: 10.3934/dcds.2008.22.1041

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

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

Received  June 2007 Revised  December 2007 Published  September 2008

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.
Citation: Ciprian G. Gal, Hao Wu. Asymptotic behavior of a Cahn-Hilliard equation with Wentzell boundary conditions and mass conservation. Discrete & Continuous Dynamical Systems - A, 2008, 22 (4) : 1041-1063. doi: 10.3934/dcds.2008.22.1041
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