Publications [#244217] of Thomas P. Witelski
search www.ams.org.Papers Published
- Bernoff, AJ; Witelski, TP, Linear stability of source-type similarity solutions of the thin film equation,
Applied Mathematics Letters, vol. 15 no. 5
(January, 2002),
pp. 599-606, Elsevier BV, ISSN 0893-9659 [doi]
(last updated on 2024/04/24)Abstract:
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 Science Ltd. All rights reserved.