Hydrodynamic scaling limit of continuum solid-on-solid model

[摘要] A fourth-order nonlinear evolution equation is derived from amicroscopic model for surface diffusion, namely, the continuumsolid-on-solid model. We use the method developed by Varadhan forthe computation of the hydrodynamic scaling limit of nongradientmodels. What distinguishes our model from other models discussedso far is the presence of two conservation laws for the dynamicsin a nonperiodic box and the complex dynamics that is notnearest-neighbor interaction. Along the way, a few steps have tobe adapted to our new context. As a byproduct of our main result,we also derive the hydrodynamic scaling limit of a perturbation ofthe continuum solid-on-solid model, a model that incorporates bothsurface diffusion and surface electromigration.

[学科分类] 应用数学