Anomalous exponents and dipole solutions for the thin film equation

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)149-179
Number of pages31
JournalSIAM Journal on Applied Mathematics
Issue number1
Publication statusPublished - 2001
Externally publishedYes


  • Asymptotic expansions
  • Four-dimensional phase space
  • Numerics
  • Self-similarity
  • Thin film equation

ASJC Scopus subject areas

  • Applied Mathematics


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