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

✍ Scribed by A.J. Bernoff; T.P. Witelski

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 522 KB
• Volume: 15
• Category: Article
• ISSN: 0893-9659
• DOI: 10.1016/s0893-9659(02)80012-x

✦ Synopsis

we study the stability of compactly-supported source-type self-similar solutions of the generalized thin film equation ht = -(hnh,,,

),. 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.