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Classical solutions
Short-time pattern formation in
thin film equations
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.