Continuum limit of a mesoscopic model with elasticity of step motion on vicinal surfaces

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.

52 pages

References in corpus (1)

• Emergence of step flow from atomistic scheme of epitaxial growth in 1+1 dimensions

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