Gradient flow approach to an exponential thin film equation: global existence and latent singularity
Published
Journal Article
In this work, we study a fourth order exponential equation, ut = Δe−Δu derived from thin film growth on crystal surface in multiple space dimensions. We use the gradient flow method in metric space to characterize the latent singularity in global strong solution, which is intrinsic due to high degeneration. We define a suitable functional, which reveals where the singularity happens, and then prove the variational inequality solution under very weak assumptions for initial data. Moreover, the existence of global strong solution is established with regular initial data.
Full Text
Duke Authors
Cited Authors
- Gao, Y; Liu, J-G; Lu, XY
Published Date
- 2019
Published In
Volume / Issue
- 25 /
Start / End Page
- 49 - 49
Published By
Electronic International Standard Serial Number (EISSN)
- 1262-3377
International Standard Serial Number (ISSN)
- 1292-8119
Digital Object Identifier (DOI)
- 10.1051/cocv/2018037