  The Cahn-Hilliard equation is the most common model to describe phase
separation processes of a mixture of two components. For a better description
of short-range interactions of the material with the solid wall, various
dynamic boundary conditions have been considered in recent times. New models
with dynamic boundary conditions have been proposed recently by C. Liu and H.
Wu [arXiv:1710.08318]. We prove the existence of weak solutions to these new
models by interpreting the problem as a suitable gradient flow of a total free
energy which contains volume as well as surface contributions. The formulation
involves an inner product which couples bulk and surface quantities in an
appropriate way. We use an implicit time discretization and show that the
obtained approximate solutions converge to a weak solution of the Cahn-Hilliard
system. This allows us to substantially improve earlier results which needed
strong assumptions on the geometry of the domain. Furthermore, we prove that
this weak solution is unique.
