- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:04
Interfaces and Free Boundaries
Interfaces Free Bound.
IFB
1463-9963
1463-9971
Partial differential equations
Numerical analysis
Fluid mechanics
Biology and other natural sciences
10.4171/IFB
http://www.ems-ph.org/doi/10.4171/IFB
subscribers, moving wall 5 years
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
16
2014
1
A Hilbert expansion method for the rigorous sharp interface limit of the generalized Cahn–Hilliard equation
Dimitra
Antonopoulou
University of Crete, HERAKLION, GREECE
Georgia
Karali
University of Crete, HERAKLION, GREECE
Enza
Orlandi
Università di Roma Tre, ROMA, ITALY
Cahn–Hilliard equation, forcing, sharp interface limit, Hilbert expansion
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].
Partial differential equations
65
104
10.4171/IFB/314
http://www.ems-ph.org/doi/10.4171/IFB/314