Short-time pattern formation in
thin film equations
Hyung Ju Hwang - Department of Mathematics, Pohang University of Science and Technology, Pohang 790-784, South Korea (email)
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.
Keywords: Thin film
equation, nonlinear stability, pattern formation
Received: December 2007; Revised: July 2008; Published: November 2008.
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