Gradient bounds for a thin film epitaxy equation

被引：17
作者：
Li, Dong [1 ]
Qiao, Zhonghua [2 ]
Tang, Tao [3 ,4 ]
机构：
[1] Univ British Columbia, Dept Math, 1984 Math Rd, Vancouver, BC V6T 1Z2, Canada
[2] Hong Kong Polytech Univ, Dept Appl Math, Hong Kong, Hong Kong, Peoples R China
[3] South Univ Sci & Technol, Dept Math, Shenzhen 518055, Guangdong, Peoples R China
[4] Hong Kong Baptist Univ, Dept Math, Kowloon, Hong Kong, Peoples R China
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2017年 / 262卷 / 03期
基金：
加拿大自然科学与工程研究理事会;
关键词：
Epitaxy; Thin film; Maximum principle; Gradient bound; CRYSTAL-SURFACES; STEP MOTION; SCHEMES; MODELS;
D O I：
10.1016/j.jde.2016.10.025
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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 wellposeciness 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. (C) 2016 Elsevier Inc. All rights reserved.
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页码：1720 / 1746
页数：27
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