Math @ Duke

Publications [#327371] of Jianfeng Lu
Papers Published
 Gao, Y; Liu, JG; Lu, J, Weak Solution of a Continuum Model For Vicinal Surface in The AttachmentDetachmentLimited Regime,
SIAM Journal on Mathematical Analysis, vol. 49 no. 3
(January, 2017),
pp. 17051731 [doi]
(last updated on 2018/03/19)
Abstract: © 2017 Society for Industrial and Applied Mathematics. We study in this work a continuum model derived from a onedimensional attachmentdetachmentlimited 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 spacetime Hölder continuity of the weak solution is also discussed as a byproduct.


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