The surface equation of motion in the continuum limit was derived by considering the diffusion of surface species along the gradient of their chemical potential in the presence of a bulk sink/source. This extended Mullins' equation and was distinct from the Cahn-Taylor equation. The characteristic length, below which this equation led to new solutions, was within the length-scale of many practical situations; for instance, low-temperature flattening. Application to thermal groove motion was considered.

Shape Evolution by Surface Diffusion A.J.Vilenkin, A.Brokman: Physical Review B, 1997, 56[15], 9871-3