**Papers Published**

- 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

(last updated on 2018/10/18)**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.