Gradient flow approach to an exponential thin film equation: Global existence and latent singularity

Journal Article (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, JG; Lu, XY

Published Date

  • January 1, 2019

Published In

Volume / Issue

  • 25 /

Electronic International Standard Serial Number (EISSN)

  • 1262-3377

International Standard Serial Number (ISSN)

  • 1292-8119

Digital Object Identifier (DOI)

  • 10.1051/cocv/2018037

Citation Source

  • Scopus