AMCA: Dynamics for a Critical-Case Unstable Generalized Thin Film Equation by Thomas Witelski

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Workshop on Patterns in Physics
November 14-18, 2003
The Fields Institute
Toronto, ON, Canada

Organizers
R. Almgren, N. Ercolani, D. Henderson, J. Lega, M. Pugh

Dynamics for a Critical-Case Unstable Generalized Thin Film Equation
by
Thomas Witelski
Duke University

We examine the dynamics of blow-up singularities in a critical-case unstable thin film equation. This is a nonlinear fourth-order degenerate parabolic PDE derived from a generalized model for the free-surface evolution of lubrication flows of thin viscous films. For a special balance between destabilizing second-order terms and regularizing fourth-order terms, this equation has a very 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.

This is joint work done with Andrew Bernoff and Andrea Bertozzi.

Date received: September 22, 2003

Copyright © 2003 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts. Document # camh-06.