  We present analytic solutions for steady flow of the Johnson-Segalman (JS)
model with a diffusion term in various geometries and under controlled strain
rate conditions, using matched asymptotic expansions. The diffusion term
represents a singular perturbation that lifts the continuous degeneracy of
stable, banded, steady states present in the absence of diffusion. We show that
the stable steady flow solutions in Poiseuille and cylindrical Couette
geometries always have two bands. For Couette flow and small curvature, two
different banded solutions are possible, differing by the spatial sequence of
the two bands.
