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Journal of Applied Mathematics
Volume 2006, Article ID 69101, 37 pages

Hydrodynamic scaling limit of continuum solid-on-solid model

Department of Mathematics, University of Northern British Columbia, Prince George, BC, Canada V2N 4Z9

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.


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.