Existence theorems for a multidimensional crystal surface model


Journal Article

© 2016 Society for Industrial and Applied Mathematics. In this paper we study the existence assertion of the initial boundary value problem for the equation @u/@t = Δe-Δu. This problem arises in the mathematical description of the evolution of crystal surfaces. Our investigations reveal that the exponent in the equation can have a singular part in the sense of the Lebesgue decomposition theorem, and the exponential nonlinearity somehow "cancels" it out. The net result is that we obtain a solution u that satisfies the equation and the initial boundary conditions in the almost everywhere (a.e.) sense.

Full Text

Duke Authors

Cited Authors

  • Liu, JG; Xu, X

Published Date

  • January 1, 2016

Published In

Volume / Issue

  • 48 / 6

Start / End Page

  • 3667 - 3687

Electronic International Standard Serial Number (EISSN)

  • 1095-7154

International Standard Serial Number (ISSN)

  • 0036-1410

Digital Object Identifier (DOI)

  • 10.1137/16M1059400

Citation Source

  • Scopus