Optimal profiles in a phase-transition model with a saturating flux

It is well known that for the Allen–Cahn equation, the minimizing transition in an infinite cylinder R×ωR×ω is one-dimensional and unique up to a translation in the first variable. We analyze in this paper the existence and symmetry of optimal profiles for transitions in a similar phase-separation model with a saturating flux. This amounts to consider transitions in the space of BV functions as we consider the area integral instead of the Dirichlet energy to penalize the creation of wild interfaces.