Continuum limit of a mesoscopic model with elasticity of step motion on vicinal surfaces
Analysis of PDEs
2022-11-08 v2 Adaptation and Self-Organizing Systems
Abstract
This work considers the rigorous derivation of continuum models of step motion starting from a mesoscopic Burton-Cabrera-Frank (BCF) type model following the work [Xiang, SIAM J. Appl. Math. 2002]. We prove that as the lattice parameter goes to zero, for a finite time interval, a modified discrete model converges to the strong solution of the limiting PDE with first order convergence rate.
Keywords
Cite
@article{arxiv.1606.08060,
title = {Continuum limit of a mesoscopic model with elasticity of step motion on vicinal surfaces},
author = {Yuan Gao and Jian-Guo Liu and Jianfeng Lu},
journal= {arXiv preprint arXiv:1606.08060},
year = {2022}
}
Comments
52 pages