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...

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Những tác giả chính: Bernoff, A, Witelski, T
Định dạng: Journal article
Ngôn ngữ:English
Được phát hành: 2002
Miêu tả
Tóm tắt: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.