  We study the well-posedness of a modified degenerate Cahn-Hilliard type model
for surface diffusion. With degenerate phase-dependent diffusion mobility and
additional stabilizing function, this model is able to give the correct sharp
interface limit. We introduce a notion of weak solutions for the nonlinear
model. The existence result is obtained by approximations of the proposed model
with nondegenerate mobilities. We also employ this method to prove existence of
weak solutions to a related model where the chemical potential contains a
nonlocal term originated from self-climb of dislocations in crystalline
materials.
