American Institute of Mathematical Sciences

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July  2009, 23(3): 867-885. doi: 10.3934/dcds.2009.23.867

Short-time pattern formation in thin film equations

Hyung Ju Hwang 1, and  Thomas P. Witelski 2,

1. 

Department of Mathematics, Pohang University of Science and Technology, Pohang 790-784, South Korea
2. 

Mathematics Department, Duke University, Box 90320, Durham, NC 27708-0320, United States

Received  December 2007 Revised  July 2008 Published  November 2008

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: nonlinear stability, Thin film equation, pattern formation.
Mathematics Subject Classification: 35K25 35B35 76A20 35G25 35K55.
Citation: Hyung Ju Hwang, Thomas P. Witelski. Short-time pattern formation in thin film equations. Discrete and Continuous Dynamical Systems, 2009, 23 (3) : 867-885. doi: 10.3934/dcds.2009.23.867
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