Paper Info
Title
Coarsening Mechanism for Systems Governed by the Cahn-Hilliard Equation with Degenerate Diffusion Mobility.
Abstract
We study a Cahn-Hilliard equation with a diffusion mobility that is degenerate in both phases and a double-well potential that is continuously differentiable. Using asymptotic analysis, we show that the interface separating the two phases does not move in the t = O(1) or O(epsilon(-1)) time scales, although in the latter regime there is a nontrivial porous medium diffusion process in both phases. Interface motion occurs in the t = O(epsilon(-2)) time scale and is determined by quasi-stationary porous medium diffusion processes in both bulk phases, together with a surface diffusion process along the interface itself. In addition, in off-critical systems where one phase-the minor phase-occupies only a small fraction of the system and consists of many disjoint components, it is the quasi-stationary porous medium diffusion process that provides communications between the disjoint components and accounts for the occurrence of coarsening.
Year
DOI
Venue
2014
10.1137/140952387
MULTISCALE MODELING & SIMULATION
Keywords
Field
DocType
Cahn-Hilliard equation,degenerate diffusion mobility,asymptotic analysis,coarsening,motion of interfaces
Diffusion process,Degenerate energy levels,Molecular diffusion,Disjoint sets,Mathematical analysis,Cahn–Hilliard equation,Porous medium,Anomalous diffusion,Mathematics,Surface diffusion
Journal
Volume
Issue
ISSN
12
4
1540-3459
Citations 
PageRank 
References 
2
0.40
0
Authors
2
Name
Order
Citations
PageRank
Shibin Dai1529.19
Qiang Du21692188.27