Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/65693
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Title: Gradient bounds for a thin film epitaxy equation
Authors: Li, D
Qiao, Z 
Tang, T
Issue Date: 5-Feb-2017
Source: Journal of differential equations, 5 Feb. 2017, v. 262, no. 3, p. 1720-1746
Abstract: We consider a gradient flow modeling the epitaxial growth of thin films with slope selection. The surface height profile satisfies a nonlinear diffusion equation with biharmonic dissipation. We establish optimal local and global wellposedness for initial data with critical regularity. To understand the mechanism of slope selection and the dependence on the dissipation coefficient, we exhibit several lower and upper bounds for the gradient of the solution in physical dimensions d≤3.
Keywords: Epitaxy
Gradient bound
Maximum principle
Thin film
Publisher: Academic Press
Journal: Journal of differential equations 
ISSN: 0022-0396
DOI: 10.1016/j.jde.2016.10.025
Rights: © 2016 Elsevier Inc. All rights reserved.
© 2016. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/.
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