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Asymptotic behavior of a Cahn-Hilliard equation with Wentzell boundary conditions and mass conservation
December  2008, 22(4): 1065-1080. doi: 10.3934/dcds.2008.22.1065

## Stable discretizations of the Cahn-Hilliard-Gurtin equations

 1 Université de Poitiers, Laboratoire de Mathématiques et Applications, Téléport 2 - BP 30179, SP2MI, Boulevard Marie et Pierre Curie, 86962 Futuroscope Chasseneuil, France 2 Laboratoire de Mathématiques et Applications UMR CNRS 6086, Université de Poitiers, Téléport 2 - BP 30179, Boulevard Marie et Pierre Curie, 86962 Futuroscope Chasseneuil, France

Received  March 2007 Revised  June 2007 Published  September 2008

We study space and time discretizations of the Cahn-Hilliard-Gurtin equations with a polynomial nonlinearity. We first consider a space semi-discrete version of the equations, and we prove in particular that any solution converges to a steady state (as in the continuous case). Then, we study the numerical stability of the fully discrete scheme obtained by applying the Euler backward scheme to the space semi-discrete problem. In particular, we show that this fully discrete problem is unconditionally stable. Numerical simulations in one space dimension conclude the paper.
Citation: Sami Injrou, Morgan Pierre. Stable discretizations of the Cahn-Hilliard-Gurtin equations. Discrete & Continuous Dynamical Systems, 2008, 22 (4) : 1065-1080. doi: 10.3934/dcds.2008.22.1065
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