The linear limit of the dipole problem for the thin film equation

Mark Bowen*, Thomas P. Witelski

*この研究の対応する著者

研究成果: Article査読

18 被引用数 (Scopus)

抄録

We investigate self-similar solutions of the dipole problem for the one-dimensional thin film equation on the half-line {x ≥ 0}. We study compactly supported solutions of the linear moving boundary problem and show how they relate to solutions of the nonlinear problem. The similarity solutions are generally of the second kind, given by the solution of a nonlinear eigenvalue problem, although there are some notable cases where first-kind solutions also arise. We examine the conserved quantities connected to these first-kind solutions. Difficulties associated with the lack of a maximum principle and the non-self-adjointness of the fundamental linear problem are also considered. Seeking similarity solutions that include sign changes yields a surprisingly rich set of (coexisting) stable solutions for the intermediate asymptotics of this problem. Our results include analysis of limiting cases and comparisons with numerical computations.

本文言語English
ページ(範囲)1727-1748
ページ数22
ジャーナルSIAM Journal on Applied Mathematics
66
5
DOI
出版ステータスPublished - 2006 10 25
外部発表はい

ASJC Scopus subject areas

  • 応用数学

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