Weak solution of a continuum model for vicinal surface in the attachment-detachment-limited regime
© 2017 Society for Industrial and Applied Mathematics. We study in this work a continuum model derived from a one-dimensional attachmentdetachment-limited type step flow on a vicinal surface, ut = -u2(u3)hhhh, where u, considered as a function of step height h, is the step slope of the surface. We formulate a notion of a 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 the weak solution and prove it converges to a constant solution as time goes to infinity. The space-time Hölder continuity of the weak solution is also discussed as a byproduct.
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