  Mass-conserving reaction-diffusion systems with bistable nonlinearity are
useful models for studying cell polarity formation, which is a key process in
cell division and differentiation. We rigorously show the existence and
stability of stationary solutions with a single internal transition layer in
such reaction-diffusion systems under general assumptions by the singular
perturbation theory. Moreover, we present a meaningful model for understanding
the existence of an unstable transition layer solution; our numerical
simulations show that the unstable solution is a separatrix of the dynamics of
the model.
