Gao, Y; Liu, J-G; Lu, J, *Weak Solution of a Continuum Model For Vicinal Surface in The Attachment-Detachment-Limited Regime*,
SIAM Journal on Mathematical Analysis, vol. 49 no. 3
(January, 2017),
pp. 1705-1731 [doi] .
**Abstract:**

*© 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, 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 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.*