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.
© 2004 Cambridge University Press
T. P. WITELSKI, A. J. BERNOFF and A. L. BERTOZZI (2004). Blowup and dissipation in a critical-case unstable thin film equation. European Journal of Applied Mathematics, , pp 223-256. doi:10.1017/S0956792504005418.