## Journal of Applied Mathematics

### Hydrodynamic scaling limit of continuum solid-on-solid model

Anamaria Savu

#### 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.

#### Article information

Source
J. Appl. Math., Volume 2006 (2006), Article ID 69101, 37 pages.

Dates
First available in Project Euclid: 16 January 2007

https://projecteuclid.org/euclid.jam/1168975518

Digital Object Identifier
doi:10.1155/JAM/2006/69101

Mathematical Reviews number (MathSciNet)
MR2231983

Zentralblatt MATH identifier
1141.82324

#### Citation

Savu, Anamaria. Hydrodynamic scaling limit of continuum solid-on-solid model. J. Appl. Math. 2006 (2006), Article ID 69101, 37 pages. doi:10.1155/JAM/2006/69101. https://projecteuclid.org/euclid.jam/1168975518

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