  We consider a class of Cahn-Hilliard equation with kinetic rate dependent
dynamic boundary conditions that describe possible short-range interactions
between the binary mixture and the solid boundary. In the presence of surface
diffusion on the boundary, the initial boundary value problem can be viewed as
a transmission problem consisting of Cahn-Hilliard type equations both in the
bulk and on the boundary. We first prove existence, uniqueness and continuous
dependence of global weak solutions. In the construction of solutions, an
explicit convergence rate in terms of the parameter for the Yosida
approximation is established. Under some additional assumptions, we also obtain
the existence and uniqueness of global strong solutions. Next, we study the
asymptotic limit as the coefficient of the boundary diffusion goes to zero and
show that the limit problem with a forward-backward dynamic boundary condition
is well-posed in a suitable weak formulation. Besides, we investigate the
asymptotic limit as the kinetic rate tends to zero and infinity, respectively.
Our results are valid for a general class of bulk and boundary potentials with
double-well structure, including the physically relevant logarithmic potential
and the non-smooth double-obstacle potential.
