SHORT-TIME PATTERN FORMATION IN THIN FILM EQUATIONS

Abstract

We study the early stages of the nonlinear dynamics of pattern formation for unstable generalized thin film equations. For unstable constant steady states, we obtain rigorous estimates for the short- to intermediate-time nonlinear evolution which extends the mathematical characterization for pattern formation derived from linear analysis: formation of patterns can be bounded by the finitely many dominant growing eigenmodes from the initial perturbation.