Hydrodynamic scaling limit of continuum solid-on-solid model

Savu, Anamaria

doi:https://doi.org/10.1155/JAM/2006/69101

Journal of Applied Mathematics

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Volume 2006 | Article ID 069101 | https://doi.org/10.1155/JAM/2006/69101

Hydrodynamic scaling limit of continuum solid-on-solid model

Anamaria Savu¹

Received01 Jun 2005

Revised09 Jan 2006

Accepted05 Mar 2006

Published06 Jun 2006

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.

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Copyright

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.

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