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http://hdl.handle.net/10397/65693
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/. |
Appears in Collections: | Journal/Magazine Article |
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a0735-n06_1208_thin_film_v3.pdf | Pre-Published version | 955.16 kB | Adobe PDF | View/Open |
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