In this talk, we study a nonstandard Cahn-Hilliard system which was introduced by P. Podio-Guidugli as a model for the separation of two species (atoms and vacancies, say) on an atomic lattice. The resulting system is a strongly nonlinear coupled system of PDEs for the unknowns, the chemical potential and the order parameter of the system (usually the density of one of the two phases). In the past years, the system was thoroughly analyzed with regard to well-posedness, asymptotics, and optimal control for the case of zero Neumann boundary conditions. In this talk, the more challenging case of dynamic boundary conditions for the order parameter is investigated. We present recent results concerning existence, regularity and optimal control. This is a joint work with Pierluigi Colli and Gianni Gilardi (Pavia, Italy).

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