Anomalous exponents and dipole solutions for the thin film equation

Mark Bowen, J. Hulshof, J. R. King

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

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
Volume62
Issue number1
Publication statusPublished - 2001
Externally publishedYes

Fingerprint

Thin Film Equation
Similarity Solution
Dipole
Anomalous
Phase Space
Exponent
Zero angle
Thin films
Contact Angle
Compact Support
Self-similarity
Asymptotic Analysis
Half line
Asymptotic analysis
Trajectory
Boundary conditions
Numerical Simulation
Contact angle
Trajectories
Computer simulation

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Anomalous exponents and dipole solutions for the thin film equation. / Bowen, Mark; Hulshof, J.; King, J. R.

In: SIAM Journal on Applied Mathematics, Vol. 62, No. 1, 2001, p. 149-179.

Research output: Contribution to journalArticle

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