A mapping of a generalisation of a thin film equation on a moving substrate

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Abstract

Lie group analysis is used to determine an invertible transformation between a generalised thin film equation ut + (α unm u / ∂ xm)x = 0 and a generalised thin film equation on a moving substrate ut + (α unm u / ∂ xm - v (t) u)x = 0 where v (t) is the substrate velocity. Consequently we obtain new solutions for the motion of a hard contact lens on a thin film of tears where α = 1 / 3, n = m = 3.

Original languageEnglish
Pages (from-to)1980-1988
Number of pages9
JournalNonlinear Analysis, Theory, Methods and Applications
Volume66
Issue number9
DOIs
Publication statusPublished - 1 May 2007
Externally publishedYes

Keywords

  • Generalised thin film equation
  • Lie group analysis
  • Moving substrate

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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