Analytical validation of a continuum model for the evolution of a crystal surface in multiple space dimensions

Jian-Guo Liu Duke University Xiangsheng Xu Mississippi State University

Analysis of PDEs mathscidoc:1702.03002

2017.2
In this paper we are concerned with the existence of a weak solution to the initial boundary value problem for the equation ∂ t u=Δ(Δu) −3 . This problem arises in the mathematical modeling of the evolution of a crystal surface. Existence of a weak solution u with Δu≥0 is obtained via a suitable substitution. Our investigations reveal the close connection between this problem and the equation ∂ t ρ+ρ 2 Δ 2 ρ 3 =0 , another crystal surface model first proposed by H. Al Hajj Shehadeh, R. V. Kohn and J. Weare in [1].
Existence, nonlinear fourth order parabolic equations, singularity, crystal surface models
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@inproceedings{jian-guo2017analytical,
  title={Analytical validation of a continuum model for the evolution of a crystal surface in multiple space dimensions},
  author={Jian-Guo Liu, and Xiangsheng Xu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170202225914251988155},
  year={2017},
}
Jian-Guo Liu, and Xiangsheng Xu. Analytical validation of a continuum model for the evolution of a crystal surface in multiple space dimensions. 2017. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170202225914251988155.
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