COARSENING MECHANISM FOR SYSTEMS GOVERNED BY THE CAHN-HILLIARD EQUATION WITH DEGENERATE DIFFUSION MOBILITY

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.