Session Cd - Interfacial & Thin-Film Instabilities.
ORAL session, Sunday, November 23
304, Moscone Center
Long-wave unstable thin film models form a subclass of Cahn-Hilliard type equations with degenerate mobility. Hocherman and Rosenau (Physica D, 67):113-125, 1993 conjectured that long-wave unstable Cahn-Hilliard type interface models develop finite time singularities when the nonlinearity in the destabilizing term grows faster at larger amplitudes than nonlinear effects in the stabilizing term. For the thin-film subclass, dimensional analysis with a constrained volume suggests a different blowup regime than conjectured in [1]. We present this analysis and discuss how, via Lyapunov function arguments, to prove this result. We also discuss, in a physical context, new weak solution theory for moving contact lines. Specific problems include gravitationally destabilized films and the gravity driven Hele-Shaw cell.