Global strong solution with BV derivatives to singular solid-on-solid model with exponential nonlinearity


Journal Article

© 2019 Elsevier Inc. In this work, we consider the one dimensional very singular fourth-order equation for solid-on-solid model in attachment-detachment-limit regime with exponential nonlinearity ht=∇⋅([Formula presented]∇e [Formula presented])=∇⋅([Formula presented]∇e−∇⋅([Formula presented])) where total energy E=∫|∇h| is the total variation of h. Using a logarithmic correction for total energy E=∫|∇h|ln⁡|∇h|dx and gradient flow structure with a suitable defined functional, we prove the one dimensional evolution variational inequality solution preserves a positive gradient hx which has upper and lower bounds but in BV space. We also obtain the global strong solution to the solid-on-solid model which allows an asymmetric singularity hxx+ to happen.

Full Text

Duke Authors

Cited Authors

  • Gao, Y

Published Date

  • September 15, 2019

Published In

Volume / Issue

  • 267 / 7

Start / End Page

  • 4429 - 4447

Electronic International Standard Serial Number (EISSN)

  • 1090-2732

International Standard Serial Number (ISSN)

  • 0022-0396

Digital Object Identifier (DOI)

  • 10.1016/j.jde.2019.05.011

Citation Source

  • Scopus