Shape evolution by surface diffusion

The surface equation of motion in the continuum limit is derived by considering the diffusion of surface species along the gradient of their chemical potential in the presence of a bulk sink/source. This equation extends Mullins's equation and is distinct from the Cahn-Taylor equation. The characteristic length below which this equation leads to new solutions is in the length scale of many practical problems, e.g., in the interpretation of low-temperature flattening experiments. As an example, we discuss the application to the thermal groove motion.