Linear Stability of Source-Type Similarity Solutions of the Thin Film Equation

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Mathematics (HMC)

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We study the stability of compactly-supported source-type self-similar solutions of the generalized thin film equation ht = −(hnhxxx)x. Using linear stability analysis, applied to the problem in similarity variables, we show that the source-type solutions are stable. These results are related to the underlying symmetries of the PDE. For the special case of n = 1, analytical results are obtained for the spectrum, and the eigenfunctions are given in terms of classical orthogonal polynomials.

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© 2002 Elsevier Ltd.

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