  We consider a mass-conserving bistable equation with a saturating flux on an
interval. This is the quasilinear analogue of the Rubinstein-Steinberg
equation, suitable for description of order parameter conserving solid-solid
phase transitions in the case of large spatial gradients in the order
parameter. We discuss stationary solutions and investigate the change in
bifurcation diagrams as the mass constraint and the length of the interval are
varied.
