  This paper is concerned with well-posedness of the Cahn-Hilliard equation
subject to a class of new dynamic boundary conditions. The system was recently
derived in Liu-Wu (Arch. Ration. Mech. Anal. 233 (2019), 167-247) via an
energetic variational approach and it naturally fulfills three physical
constraints such as mass conservation, energy dissipation and force balance.
The target problem examined in this paper can be viewed as a transmission
problem that consists of Cahn-Hilliard type equations both in the bulk and on
the boundary. In our approach, we are able to deal with a general class of
potentials with double-well structure, including the physically relevant
logarithmic potential and the non-smooth double-obstacle potential. Existence,
uniqueness and continuous dependence of global weak solutions are established.
The proof is based on a novel time-discretization scheme for the approximation
of the continuous problem. Besides, a regularity result is shown with the aim
of obtaining a strong solution to the system.
