Analytical validation of a 2+1 dimensional continuum model for epitaxial\n growth with elastic substrate

2016/04/29 by Elisa Davoli, Xin Lü, Davoli, Elisa +1
Computer Science · Engineering · Materials Science · #35K55 #35K67 #44A15 #74K35 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Thin Films #Solidification and crystal growth phenomena

paper · pdf · doi:10.48550/arxiv.1604.08884

openalex publication_date 2016/04/29 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

An analytical validation is obtained for the evolution equation h_t=
Delta[\n
mathcalF^-1(-aE
mathcalF(h)) - r/h² -
Delta h ], introduced in\n citeTS by W.T. Tekalign and B.J. Spencer to describe the heteroepitaxial\ngrowth of a two-dimensional thin film on an elastic substrate. In the\nexpression above, h denotes the surface height of the film, \F is\nthe Fourier transform, and a, E, r are positive material constants.\nExistence, uniqueness, and Lipschitz regularity in time for weak solutions are\nproved, under suitable assumptions on the initial datum.\n

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