Continuum Limit of a Mesoscopic Model with Elasticity of Step Motion on Vicinal Surfaces
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2016-12-29
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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.
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Gao, Y, JG Liu and J Lu (2016). Continuum Limit of a Mesoscopic Model with Elasticity of Step Motion on Vicinal Surfaces. Journal of Nonlinear Science. pp. 1–54. 10.1007/s00332-016-9354-1 Retrieved from https://hdl.handle.net/10161/14280.
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