Blowup and dissipation in a critical-case unstable thin film equation

Journal Article (Journal Article)

We study the dynamics of dissipation and blow-up in a critical-case unstable thin film equation. The governing equation is a nonlinear fourth-order degenerate parabolic PDE derived from a generalized model for lubrication flows of thin viscous fluid layers on solid surfaces. There is a critical mass for blow-up and a rich set of dynamics including families of similarity solutions for finite-time blow-up and infinite-time spreading. The structure and stability of the steady-states and the compactly-supported similarity solutions is studied.

Full Text

Duke Authors

Cited Authors

  • Witelski, TP; Bernoff, AJ; Bertozzi, AL

Published Date

  • April 1, 2004

Published In

Volume / Issue

  • 15 / 2

Start / End Page

  • 223 - 256

International Standard Serial Number (ISSN)

  • 0956-7925

Digital Object Identifier (DOI)

  • 10.1017/S0956792504005418

Citation Source

  • Scopus