Duke Applied Mathematics

Publications [#244255] of Thomas P. Witelski

Papers Published

1. Witelski, TP; Bernoff, AJ; Bertozzi, AL, Blowup and dissipation in a critical-case unstable thin film equation, European Journal of Applied Mathematics, vol. 15 no. 2 (April, 2004), pp. 223-256, Cambridge University Press (CUP) [doi]
   (last updated on 2024/04/24)

   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.