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