Gradient bounds for a thin film epitaxy equation

Dong Li; Zhonghua Qiao; Tao Tang

doi:10.1016/j.jde.2016.10.025

Gradient bounds for a thin film epitaxy equation

Dong Li, Zhonghua Qiao^*, Tao Tang

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

15 Citations (Scopus)

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.

Original language	English
Pages (from-to)	1720-1746
Number of pages	27
Journal	Journal of Differential Equations
Volume	262
Issue number	3
DOIs	https://doi.org/10.1016/j.jde.2016.10.025
Publication status	Published - 5 Feb 2017

Scopus Subject Areas

Analysis
Applied Mathematics

User-Defined Keywords

Epitaxy
Gradient bound
Maximum principle
Thin film

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10.1016/j.jde.2016.10.025

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title = "Gradient bounds for a thin film epitaxy equation",

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",

author = "Dong Li and Zhonghua Qiao and Tao Tang",

note = "Funding Information: D. Li was supported in part by an Nserc discovery grant . The research of Z. Qiao is partially supported by Hong Kong Research Council GRF grant PolyU 15302214 , and NSFC/RGC Joint Research Scheme N_HKBU204/12 . The research of T. Tang is mainly supported by Hong Kong Research Council GRF Grants and Hong Kong Baptist University FRG grants. ",

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AU - Li, Dong

AU - Qiao, Zhonghua

AU - Tang, Tao

N1 - Funding Information: D. Li was supported in part by an Nserc discovery grant . The research of Z. Qiao is partially supported by Hong Kong Research Council GRF grant PolyU 15302214 , and NSFC/RGC Joint Research Scheme N_HKBU204/12 . The research of T. Tang is mainly supported by Hong Kong Research Council GRF Grants and Hong Kong Baptist University FRG grants.

PY - 2017/2/5

Y1 - 2017/2/5

N2 - 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.

AB - 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.

KW - Epitaxy

KW - Gradient bound

KW - Maximum principle

KW - Thin film

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U2 - 10.1016/j.jde.2016.10.025

DO - 10.1016/j.jde.2016.10.025

M3 - Journal article

AN - SCOPUS:85006042848

SN - 0022-0396

VL - 262

SP - 1720

EP - 1746

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 3

ER -

Gradient bounds for a thin film epitaxy equation

Abstract

Scopus Subject Areas

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