Maximal monotone operator theory and its applications to thin film equation in epitaxial growth on vicinal surface

Journal Article (Journal Article)

In this work we consider (Formula presented.) which is derived from a thin film equation for epitaxial growth on vicinal surface. We formulate the problem as the gradient flow of a suitably-defined convex functional in a non-reflexive space. Then by restricting it to a Hilbert space and proving the uniqueness of its sub-differential, we can apply the classical maximal monotone operator theory. The mathematical difficulty is due to the fact that w can appear as a positive Radon measure. We prove the existence of a global strong solution with hidden singularity. In particular, (1) holds almost everywhere when w is replaced by its absolutely continuous part. hh hh

Full Text

Duke Authors

Cited Authors

  • Gao, Y; Liu, JG; Lu, XY; Xu, X

Published Date

  • April 1, 2018

Published In

Volume / Issue

  • 57 / 2

International Standard Serial Number (ISSN)

  • 0944-2669

Digital Object Identifier (DOI)

  • 10.1007/s00526-018-1326-x

Citation Source

  • Scopus