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arXiv · 1609.05853

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

Yuan Gao·Jian-Guo Liu·Jianfeng Lu
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Abstract

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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Yuan Gao, Jian-Guo Liu, Jianfeng Lu. 2016-09-19. Weak solution of a continuum model for vicinal surface in the attachment-detachment-limited regime. https://doi.org/10.1137/16m1094543

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