Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/65693
Title: Gradient bounds for a thin film epitaxy equation
Authors: Li, D
Qiao, Z 
Tang, T
Keywords: Epitaxy
Gradient bound
Maximum principle
Thin film
Issue Date: 2017
Publisher: Academic Press
Source: Journal of differential equations, 2017, v. 262, no. 3, p. 1720-1746 How to cite?
Journal: Journal of differential equations 
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.
URI: http://hdl.handle.net/10397/65693
ISSN: 0022-0396
DOI: 10.1016/j.jde.2016.10.025
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