Abstract
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.