"Blowup and Dissipation in a Critical-Case Unstable Thin Film Equation" by Thomas P. Witelski, Andrew J. Bernoff et al.
 

Document Type

Article

Department

Mathematics (HMC)

Publication Date

2004

Abstract

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.

Rights Information

© 2004 Cambridge University Press

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