  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 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. Along
the way, a few steps has 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 continuum solid-on-solid model, a model that incorporates both surface
diffusion and surface electromigration.
