We study the coarsening of solutions of two models of multicomponent phase separation. One is a constant mobility system; the other is a degenerate mobility system. These models are natural generalizations of the Cahn–Hilliard equation to the case of a vector-valued order parameter. It has been conjectured that the characteristic length scale l(t) grows like t1/3 as t→∞ for the first case and l∼t1/4 for the second case. We prove a weak one-sided version of this assertion. Our method follows a strategy introduced by Kohn and Otto for problems with a scalar-valued order parameter; it combines a dissipation relationship with an isoperimetric inequality and an ODE argument. We also address a related model for anisotropic epitaxial growth.
Robert V. Kohn; Xiaodong Yan. Coarsening rates for models of multicomponent phase separation. Interfaces and free boundaries, Tome 6 (2004) no. 1, pp. 135-149. doi: 10.4171/ifb/94
@article{10_4171_ifb_94,
author = {Robert V. Kohn and Xiaodong Yan},
title = {Coarsening rates for models of multicomponent phase separation},
journal = {Interfaces and free boundaries},
pages = {135--149},
year = {2004},
volume = {6},
number = {1},
doi = {10.4171/ifb/94},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/94/}
}
TY - JOUR
AU - Robert V. Kohn
AU - Xiaodong Yan
TI - Coarsening rates for models of multicomponent phase separation
JO - Interfaces and free boundaries
PY - 2004
SP - 135
EP - 149
VL - 6
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.4171/ifb/94/
DO - 10.4171/ifb/94
ID - 10_4171_ifb_94
ER -
%0 Journal Article
%A Robert V. Kohn
%A Xiaodong Yan
%T Coarsening rates for models of multicomponent phase separation
%J Interfaces and free boundaries
%D 2004
%P 135-149
%V 6
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4171/ifb/94/
%R 10.4171/ifb/94
%F 10_4171_ifb_94
