We prove an upper bound on the coarsening rate for solutions of a phase field model with arbitrarily complicated patterns of phases. The analysis is performed in a regime corresponding to the late stages of phase separation, in which the ratio between the transition layer thickness and the length scale of the pattern is small, and is also small compared to the square of the ratio between the pattern scale and the system size. The analysis extends the method of Kohn and Otto (Comm.\ Math.\ Phys.\ 229 (2002), 375-395) to deal with both temperature and phase fields.
1
University of Maryland, College Park, USA
2
Carnegie Mellon University, Pittsburgh, USA
Shibin Dai; Robert L. Pego. An upper bound on the coarsening rate for mushy zones in a phase-field model. Interfaces and free boundaries, Tome 7 (2005) no. 2, pp. 187-197. doi: 10.4171/ifb/120
@article{10_4171_ifb_120,
author = {Shibin Dai and Robert L. Pego},
title = {An upper bound on the coarsening rate for mushy zones in a phase-field model},
journal = {Interfaces and free boundaries},
pages = {187--197},
year = {2005},
volume = {7},
number = {2},
doi = {10.4171/ifb/120},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/120/}
}
TY - JOUR
AU - Shibin Dai
AU - Robert L. Pego
TI - An upper bound on the coarsening rate for mushy zones in a phase-field model
JO - Interfaces and free boundaries
PY - 2005
SP - 187
EP - 197
VL - 7
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.4171/ifb/120/
DO - 10.4171/ifb/120
ID - 10_4171_ifb_120
ER -
%0 Journal Article
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%A Robert L. Pego
%T An upper bound on the coarsening rate for mushy zones in a phase-field model
%J Interfaces and free boundaries
%D 2005
%P 187-197
%V 7
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4171/ifb/120/
%R 10.4171/ifb/120
%F 10_4171_ifb_120
