Coarsening rates for models of multicomponent phase separation
Robert V. KohnNew York University, USA
Xiaodong YanNew York University, USA
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 grows like as for the first case and 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.
Cite this article
Robert V. Kohn, Xiaodong Yan, Coarsening rates for models of multicomponent phase separation. Interfaces Free Bound. 6 (2004), no. 1, pp. 135–149DOI 10.4171/IFB/94