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.
ASJC Scopus subject areas
- Surfaces and Interfaces