Linear Stability of Source-Type Similarity Solutions of the Thin Film Equation

Authors

Andrew J. Bernoff, Harvey Mudd CollegeFollow
Thomas P. Witelski, Duke University

Document Type

Article

Department

Mathematics (HMC)

Publication Date

2002

Abstract

We study the stability of compactly-supported source-type self-similar solutions of the generalized thin film equation h_t = −(hⁿh_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.

Rights Information

© 2002 Elsevier Ltd.

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

DOI

10.1016/S0893-9659(02)80012-X

Recommended Citation

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)