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Existence and uniqueness of solutions for nonlocal Cahn-Hilliard equationswith degenerate potential is shown. The nonlocality is described by means of asymmetric singular kernel not falling within the framework of any previousexistence theory. A convection term is also taken into account. Building uponthis novel existence result, we prove convergence of solutions for this classof nonlocal Cahn-Hilliard equations to their local counterparts, as thenonlocal convolution kernels approximate a Dirac delta. Eventually, we showthat, under suitable assumptions on the data, the solutions to the nonlocalCahn-Hilliard equations exhibit further regularity, and the nonlocal-to-localconvergence is verified in a stronger topology.

Degenerate nonlocal Cahn-Hilliard equations: well-posedness, regularity and local asymptotics