Short-time pattern formation inthin film equations

Hyung Ju Hwang; Thomas P. Witelski

doi:10.3934/dcds.2009.23.867

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2009, Volume 23, Issue 3: 867-885. Doi: 10.3934/dcds.2009.23.867

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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
2.
Mathematics Department, Duke University, Box 90320, Durham, NC 27708-0320

Received: November 30, 2007

Revised: June 30, 2008

Published: August 2009

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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.

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Mathematics Subject Classification: 35K25 35B35 76A20 35G25 35K55.

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