Journal of Nonlinear Science

, Volume 27, Issue 3, pp 873–926 | Cite as

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

  • Yuan Gao
  • Jian-Guo Liu
  • Jianfeng Lu


This work considers the rigorous derivation of continuum models of step motion starting from a mesoscopic Burton–Cabrera–Frank-type model following the Xiang’s work (Xiang in SIAM J Appl Math 63(1):241–258, 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 

Mathematics Subject Classification

35K25 35K55 74A50 



We would like to thank the support by the National Science Foundation under Grants DMS-1514826 (JGL), DMS-1454939 (JL), and also through the research network KI-Net RNMS11-07444. We thank Dionisios Margetis, Jeremy Marzuola, Yang Xiang and Aaron N.K. Yip for helpful discussions.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.School of Mathematical SciencesFudan UniversityShanghaiPeople’s Republic of China
  2. 2.Department of MathematicsDuke UniversityDurhamUSA
  3. 3.Department of PhysicsDuke UniversityDurhamUSA
  4. 4.Department of ChemistryDuke UniversityDurhamUSA

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