Analytical validation of a continuum model for the evolution of a crystal surface in multiple space dimensions


Journal Article

© 2017 Society for Industrial and Applied Mathematics. In this paper we are concerned with the existence of a weak solution to the initial boundary value problem for the equation ∂u/∂t = Δ(Δu)-3. This problem arises in the mathematical modeling of the evolution of a crystal surface. Existence of a weak solution u with Δu ≥ 0 is obtained via a suitable substitution. Our investigations reveal the close connection between this problem and the equation ∂tρ+ρ2Δ2ρ3 = 0, another crystal surface model first proposed by H. Al Hajj Shehadeh, R. V. Kohn, and J. Weare [Phys. D, 240 (2011), pp. 1771-1784].

Full Text

Duke Authors

Cited Authors

  • Liu, JG; Xu, X

Published Date

  • January 1, 2017

Published In

Volume / Issue

  • 49 / 3

Start / End Page

  • 2220 - 2245

Electronic International Standard Serial Number (EISSN)

  • 1095-7154

International Standard Serial Number (ISSN)

  • 0036-1410

Digital Object Identifier (DOI)

  • 10.1137/16M1098474

Citation Source

  • Scopus