Weak solution of a continuum model for vicinal surface in the attachment-detachment-limited regime

Yuan Gao Fudan University Jian-Guo Liu Duke University Jianfeng Lu Duke University

Analysis of PDEs mathscidoc:1702.03007

2017.1
We study in this work a continuum model derived from 1D attachment-detachment-limited (ADL) type step flow on vicinal surface, $ u_t=-u^2(u^3)_{hhhh}$, where $u$, considered as a function of step height $h$, is the step slope of the surface. We formulate a notion of weak solution to this continuum model and prove the existence of a global weak solution, which is positive almost everywhere. We also study the long time behavior of weak solution and prove it converges to a constant solution as time goes to infinity. The space-time H\"older continuity of the weak solution is also discussed as a byproduct.
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@inproceedings{yuan2017weak,
  title={Weak solution of a continuum model for vicinal surface in the attachment-detachment-limited regime},
  author={Yuan Gao, Jian-Guo Liu, and Jianfeng Lu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170206150241624819190},
  year={2017},
}
Yuan Gao, Jian-Guo Liu, and Jianfeng Lu. Weak solution of a continuum model for vicinal surface in the attachment-detachment-limited regime. 2017. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170206150241624819190.
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