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Publication 120

Regularity In Time for Weak Solutions of a Continuum Model for Epitaxial Growth with Elasticity on Vicinal Surfaces

Authors:

CMUIrene Fonseca
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213


CMUGiovanni Leoni
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213


CMUXin Yang Lu
Department of Mathematical Sciences
Carnegie Mellon University


Abstract:
The evolution equation derived by Xiang (SIAM J. Appl. Math. 63:241-258, 2002) to describe vicinal surfaces in heteroepitaxial growth is $$ht = - \left[H(h_x) + (h^{-1}_2 + h_x)H_{xx}\right]_{xx}, {(1)}$$ where $h$ denotes the surface height of the film, and $H$ is the Hilbert transform. Existence of solutions was obtained by Dal Maso, Fonseca and Leoni (Arch. Rational Mech. Anal. 212: 1037-1064, 2014). The regularity in time was left unresolved. The aim of this paper is to prove existence, uniqueness, and Lipschitz regularity in time for weak solutions, under suitable assumptions on the initial datum.
Get the paper in its entirety
15-CNA-015.pdf

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