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

Mark Bowen, Thomas P. Witelski

研究成果: Article

18 引用 (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.

元の言語English
ページ(範囲)1727-1748
ページ数22
ジャーナルSIAM Journal on Applied Mathematics
66
発行部数5
DOI
出版物ステータスPublished - 2006
外部発表Yes

Fingerprint

Thin Film Equation
Dipole
Similarity Solution
Thin films
Moving Boundary Problem
Nonlinear Eigenvalue Problem
Maximum principle
Conserved Quantity
Stable Solution
Self-similar Solutions
Sign Change
Maximum Principle
Numerical Computation
Nonlinear Problem
Half line
Limiting

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

これを引用

The linear limit of the dipole problem for the thin film equation. / Bowen, Mark; Witelski, Thomas P.

:: SIAM Journal on Applied Mathematics, 巻 66, 番号 5, 2006, p. 1727-1748.

研究成果: Article

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