- Thomas P. Witelski and Andrew J. Bernoff and Andrea L. Bertozzi, Blowup and dissipation in a critical-case unstable thin film equation,
European Journal of Applied Mathematics, vol. 15 no. 2
pp. 223-256 .
(last updated on 2004/06/08)
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.