Hydrodynamic Scaling Limit of Continuum Solid-on-solid Model

A fourth-order nonlinear evolution equation is derived from a microscopic model for surface diffusion, namely, the continuum solid-on-solid model. We use the method developed by Varadhan for the computation of the hydrodynamic scaling limit of nongradient models. What distinguishes our model from other models discussed so far is the presence of two conservation laws for the dynamics in a nonperiodic box and the complex dynamics that is not nearest-neighbor interaction. Along the way, a few steps have to be adapted to our new context. As a byproduct of our main result, we also derive the hydrodynamic scaling limit of a perturbation of the continuum solid-on-solid model, a model that incorporates both surface diffusion and surface electromigration.