Homogenization of one-phase Stefan-type problems in periodic and random media

Abstract

We investigate the homogenization of Stefan-type problems with oscillating diffusion coefficients. Both cases of periodic and random (stationary ergodic) mediums are considered. The proof relies on the coincidence of viscosity solutions and weak solutions (which are the time derivatives of the solutions of an obstacle problem) for the Stefan problem. This coincidence result is of independent interest.