Weak solution of a continuum model for vicinal surface in the attachment-detachment-limited regime

Published

Journal Article

© 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.

Full Text

Duke Authors

Cited Authors

  • Gao, Y; Liu, JG; Lu, J

Published Date

  • January 1, 2017

Published In

Volume / Issue

  • 49 / 3

Start / End Page

  • 1705 - 1731

Electronic International Standard Serial Number (EISSN)

  • 1095-7154

International Standard Serial Number (ISSN)

  • 0036-1410

Digital Object Identifier (DOI)

  • 10.1137/16M1094543

Citation Source

  • Scopus