Analytical Validation of a Continuum Model for the Evolution of a Crystal Surface in Multiple Space Dimensions

DOI10.1137/16M1098474zbMath1371.35142arXiv1612.04269MaRDI QIDQ5270348

Xiangsheng Xu, Jian-Guo Liu

Publication date: 23 June 2017

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1612.04269

zbMATH Keywords

existencesingularitynonlinear fourth-order parabolic equationscrystal surface models

Mathematics Subject Classification ID

Existence problems for PDEs: global existence, local existence, non-existence (35A01) Partial differential equations of mathematical physics and other areas of application (35Q99) Weak solutions to PDEs (35D30) Higher-order parabolic equations (35K25)

Related Items (8)

Existence Theorems for a Crystal Surface Model Involving the $p$-Laplace Operator ⋮ Analysis of a fourth-order exponential PDE arising from a crystal surface jump process with metropolis-type transition rates ⋮ Regularity and monotonicity for solutions to a continuum model of epitaxial growth with nonlocal elastic effects ⋮ Analysis of a continuum theory for broken bond crystal surface models with evaporation and deposition effects ⋮ Mathematical validation of a continuum model for relaxation of interacting steps in crystal surfaces in 2 space dimensions ⋮ Global existence and decay to equilibrium for some crystal surface models ⋮ Maximal monotone operator theory and its applications to thin film equation in epitaxial growth on vicinal surface ⋮ A proximal-gradient algorithm for crystal surface evolution

Cites Work

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• The evolution of a crystal surface: analysis of a one-dimensional step train connecting two facets in the ADL regime
• Higher order nonlinear degenerate parabolic equations
• From crystal steps to continuum laws: behavior near large facets in one dimension
• Continuum limit of a mesoscopic model with elasticity of step motion on vicinal surfaces
• Analytical validation of a continuum model for epitaxial growth with elasticity on vicinal surfaces
• Existence Theorems for a Multidimensional Crystal Surface Model
• Derivation of a Continuum Model for Epitaxial Growth with Elasticity on Vicinal Surface
• Derivation of a Continuum Model for the Long-Range Elastic Interaction on Stepped Epitaxial Surfaces in $2+1$ Dimensions
• Weak Solution of a Continuum Model For Vicinal Surface in The Attachment-Detachment-Limited Regime
• The growth of crystals and the equilibrium structure of their surfaces

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