Anomalous exponents and dipole solutions for the thin film equation

M. Bowen, J. Hulshof, J. R. King

研究成果: Article査読

15 被引用数 (Scopus)

抄録

We investigate similarity solutions of the "thin film" equation. In particular we look at solutions on the half-line x ≥ 0 with compact support and zero contact angle boundary conditions in x = 0. Such "dipole" solutions feature an anomalous exponent and are therefore called similarity solutions of the second kind. Using a combination of phase space analysis and numerical simulations, we numerically construct trajectories representing these solutions, at the same time obtaining broader insight into the nature of the four-dimensional phase space. Additional asymptotic analysis provides further information concerning the evolution to self-similarity.

本文言語English
ページ(範囲)149-179
ページ数31
ジャーナルSIAM Journal on Applied Mathematics
62
1
DOI
出版ステータスPublished - 2001
外部発表はい

ASJC Scopus subject areas

  • 応用数学

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