Journal of Applied Mathematics
Volume 2006 (2006), Article ID 69101, 37 pages
doi:10.1155/JAM/2006/69101
Hydrodynamic scaling limit of continuum solid-on-solid model
Department of Mathematics, University of Northern British Columbia, Prince George V2N 4Z9, BC, Canada
Received 1 June 2005; Revised 9 January 2006; Accepted 5 March 2006
Copyright © 2006 Anamaria Savu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.