A vicinal surface model for epitaxial growth with logarithmic free energy


Journal Article

© 2018 American Institute of Mathematical Sciences. All Rights Reserved. We study a continuum model for solid films that arises from the modeling of one-dimensional step flows on a vicinal surface in the attachment-detachment-limited regime. The resulting nonlinear partial differential equation, ut = -u2(u3 + au)hhhh, gives the evolution for the surface slope u as a function of the local height h in a monotone step train. Subject to periodic boundary conditions and positive initial conditions, we prove the existence, uniqueness and positivity of global strong solutions to this PDE using two Lyapunov energy functions. The long time behavior of u converging to a constant that only depends on the initial data is also investigated both analytically and numerically.

Full Text

Duke Authors

Cited Authors

  • Gao, Y; Ji, H; Liu, JG; Witelski, TP

Published Date

  • December 1, 2018

Published In

Volume / Issue

  • 23 / 10

Start / End Page

  • 4433 - 4453

International Standard Serial Number (ISSN)

  • 1531-3492

Digital Object Identifier (DOI)

  • 10.3934/dcdsb.2018170

Citation Source

  • Scopus