  We consider a class of nonlocal viscous Cahn-Hilliard equations with Neumann
boundary conditions for the chemical potential. The double-well potential is
allowed to be singular (e.g. of logarithmic type), while the singularity of the
convolution kernel does not fall in any available existence theory under
Neumann boundary conditions. We prove well-posedness for the nonlocal equation
in a suitable variational sense. Secondly, we show that the solutions to the
nonlocal equation converge to the corresponding solutions to the local
equation, as the convolution kernels approximate a Dirac delta. The asymptotic
behaviour is analyzed by means of monotone analysis and Gamma convergence
results, both when the limiting local Cahn-Hilliard equation is of viscous type
and of pure type.
