= Quasisteady sliding collar on a coated cylinder
A large collar translating slowly at speed $c$ over a film $h_+$ and leaving a thinner film $h_-$ must grow: its leading excess volume increases at rate $c(h_+-h_-)$. An exact <travelling wave> connecting unequal stationary films is impossible, since integration of the <thin-film equation> would give a common constant $q-ch=-ch_+=-ch_-$. In a slowly evolving collar core the leading <pressure> gradient vanishes. Therefore $h'+h'''=0$, and a centred, reflection-symmetric collar has $h=A(1+\cos x)+B$ on $-\pi<x<\pi$. Its leading volume is $2\pi A$, so for constant small $B$, $2\pi\dot A\simeq c(h_+-h_-)$. The speed is supplied by <collar-to-film capillary matching>.
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