  In this paper we deal with a doubly nonlinear Cahn-Hilliard system, where
both an internal constraint on the time derivative of the concentration and a
potential for the concentration are introduced. The definition of the chemical
potential includes two regularizations: a viscosity and a diffusive term. First
of all, we prove existence and uniqueness of a bounded solution to the system
using a nonstandard maximum-principle argument for time-discretizations of
doubly nonlinear equations. Possibly including singular potentials, this novel
result brings improvements over previous approaches to this problem. Secondly,
under suitable assumptions on the data, we show the convergence of solutions to
the respective limit problems once either of the two regularization parameters
vanishes.
