A mapping of a generalisation of a thin film equation on a moving substrate Original Research Article

Lie group analysis is used to determine an invertible transformation between a generalised thin film equation ut+(αun∂mu/∂xm)x=0ut+(αun∂mu/∂xm)x=0 and a generalised thin film equation on a moving substrate ut+(αun∂mu/∂xm−v(t)u)x=0ut+(αun∂mu/∂xm−v(t)u)x=0 where v(t)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=1/3α=1/3, n=m=3n=m=3.