Linear stability of source-type similarity solutions of the thin film equation Original Research Article

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.