Continuum Limit of a Mesoscopic Model with Elasticity of Step Motion on Vicinal Surfaces

Yuan Gao Fudan University Jian-Guo Liu Duke University Jianfeng Lu Duke University

Analysis of PDEs mathscidoc:1702.03008

Distinguished Paper Award in 2017

Journal of Nonlinear Science, 1-54, 2017.1
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.
Epitaxial growth · BCF · Hilbert transformation · Convergence rate positivity
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@inproceedings{yuan2017continuum,
  title={Continuum Limit of a Mesoscopic Model with Elasticity of Step Motion on Vicinal Surfaces},
  author={Yuan Gao, Jian-Guo Liu, and Jianfeng Lu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170206154738488101194},
  booktitle={Journal of Nonlinear Science},
  pages={1-54},
  year={2017},
}
Yuan Gao, Jian-Guo Liu, and Jianfeng Lu. Continuum Limit of a Mesoscopic Model with Elasticity of Step Motion on Vicinal Surfaces. 2017. In Journal of Nonlinear Science. pp.1-54. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170206154738488101194.
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