Irene Fonseca: Phase Separation in Heterogeneous Media

A variational model in the context of the gradient theory for fluid-fluid phase transitions with small scale heterogeneities is studied. Two regimes are considered. Firstly, when the scale of the heterogeneities is of the same order of the scale governing the diffuse interface between the phases, it is shown that the interaction between homogenization and the phase transition process leads to an anisotropic interfacial energy. Bounds on the homogenized surface tension are established. Secondly, when the wells are allowed to move and display discontinuities, and when phase separation occurs at a smaller case than homogenization, the zeroth and first order Γ-limits are identified. In addition, a characterization of the large-scale limiting behavior of viscosity solutions to non-degenerate and periodic Eikonal equations in half-spaces is given.