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Short-time pattern formation in thin film equations

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

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