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Existence and regularity of weak solutions to a model for coarsening in molecular beam epitaxy
Author(s) -
Zhang Jun,
Zhu Peicheng
Publication year - 2012
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2648
Subject(s) - molecular beam epitaxy , uniqueness , homogeneous space , mathematics , pyramid (geometry) , growth model , surface (topology) , surface diffusion , diffusion , boundary value problem , weak solution , condensed matter physics , mathematical analysis , chemistry , epitaxy , thermodynamics , geometry , physics , materials science , mathematical economics , nanotechnology , layer (electronics) , adsorption
Taking into account the occurrence of a zero of the surface diffusion current and the requirement of the Ehrlich–Schwoebel effect, Siegert et al . formulated a model of Langevin type that describes the growth of pyramid‐like structures on a surface under conditions of molecular beam epitaxy and that the slope of these pyramids is selected by the crystalline symmetries of the growing film. In this article, the existence and uniqueness of weak solution to an initial boundary value problem for this model is proved, in the case that the noise is neglected. The regularity of the weak solution to models, with/without slope selection, is also investigated. Copyright © 2012 John Wiley & Sons, Ltd.