Math @ Duke

Publications [#329524] of JianGuo Liu
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, Society for Industrial & Applied Mathematics (SIAM) [doi]
(last updated on 2019/06/25)
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, 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 spacetime Hölder continuity of the weak solution is also discussed as a byproduct.


dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
 
Mathematics Department
Duke University, Box 90320
Durham, NC 277080320

