Geometrical flows of phase boundaries and Ginzburg-Landau systems

Phase boundary phenomena can occur in many physical systems such as in models of alloys, in certain chemical engineering systems and in superconductors, due to "bistability", the coexistence of two (or more) stable phases in the same material. If the two phases are present initially, one will observe "phase separation" on a rapid scale, creating domains of a single phase, followed by a slow "coarsening" process where the interfaces separating the domains evolve according to some geometrical law. In this talk we will see how these evolutions can be obtained as asymptotic limits of certain Ginzburg-Landau models.