Linear Stability of Source-Type Similarity Solutions of the Thin Film Equation
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.
© 2002 Elsevier Ltd.
A.J. Bernoff, T.P. Witelski, Linear stability of source-type similarity solutions of the thin film equation, Applied Mathematics Letters, Volume 15, Issue 5, July 2002, Pages 599-606, ISSN 0893-9659, 10.1016/S0893-9659(02)80012-X. (http://www.sciencedirect.com/science/article/pii/S089396590280012X)