Abstract
Lie group analysis is used to determine an invertible transformation between a generalised thin film equation ut + (α un ∂m u / ∂ xm)x = 0 and a generalised thin film equation on a moving substrate ut + (α un ∂m 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 language | English |
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Pages (from-to) | 1980-1988 |
Number of pages | 9 |
Journal | Nonlinear Analysis, Theory, Methods and Applications |
Volume | 66 |
Issue number | 9 |
DOIs | |
Publication status | Published - 1 May 2007 |
Externally published | Yes |
Keywords
- Generalised thin film equation
- Lie group analysis
- Moving substrate
ASJC Scopus subject areas
- Analysis
- Applied Mathematics