Geodesic
A Hilbert expansion method for the rigorous sharp interface limit of the generalized Cahn–Hilliard equation
Dimitra C. Antonopoulou1 ; Georgia Karali1 ; Enza Orlandi2
1University of Crete, Heraklion, Greece
2Università di Roma Tre, Italy
Interfaces and free boundaries, Tome 16 (2014) no. 1, pp. 65-104

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We consider Cahn–Hilliard equations with external forcing terms. Energy decreasing and mass conservation might not hold. We show that level surfaces of the solutions of such generalized Cahn–Hilliard equations tend to the solutions of a moving boundary problem under the assumption that classical solution of the latter exists. Our strategy is to construct approximate solutions of the generalized Cahn–Hilliard equation by the Hilbert expansion method used in kinetic theory and proposed for the standard Cahn–Hilliard equation, by Carlen, Carvalho and Orlandi, [14]. The constructed approximate solutions allow to derive rigorously the sharp interface limit of the generalized Cahn–Hilliard equations and higher order corrections to the limiting motion. We then estimate the difference between the true solutions and the approximate solutions by spectral analysis, as in [1].
DOI : 10.4171/ifb/314
Classification : 35-XX
Mots-clés : Cahn–Hilliard equation, forcing, sharp interface limit, Hilbert expansion

Dimitra C. Antonopoulou  1   ; Georgia Karali  1   ; Enza Orlandi  2

1 University of Crete, Heraklion, Greece
2 Università di Roma Tre, Italy 
Dimitra C. Antonopoulou; Georgia Karali; Enza Orlandi. A Hilbert expansion method for the rigorous sharp interface limit of the generalized Cahn–Hilliard equation. Interfaces and free boundaries, Tome 16 (2014) no. 1, pp. 65-104. doi: 10.4171/ifb/314
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     title = {A {Hilbert} expansion method for the rigorous sharp interface limit of the generalized {Cahn{\textendash}Hilliard} equation},
     journal = {Interfaces and free boundaries},
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