Papers Published

  1. A. J. Bernoff and Thomas P. Witelski, Linear stability of source-type similarity solutions of the thin film equation, Applied Mathematics Letters 18 (2002) pp. 599--606. .
    (last updated on 2002/08/21)

    We study the stability of compactly-supported source-type self-similar solutions of the generalized lubrication equation $h_t=-(h^nh_{xxx})_x$. 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.