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

Abstract:

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 quantitie...

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Publication status:
Published

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Publisher copy:
10.1137/050637832

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Journal:
SIAM JOURNAL ON APPLIED MATHEMATICS
Volume:
66
Issue:
5
Pages:
1727-1748
Publication date:
2006
DOI:
EISSN:
1095-712X
ISSN:
0036-1399
URN:
uuid:05853f26-da29-49d4-b6a2-d870840b8e3f
Source identifiers:
26116
Local pid:
pubs:26116

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