  Starting from a simple mechanical constitutive model (the non-local diffusive
Johnson-Segalman model; DJS model), we provide a rigorous theoretical
explanation as to why a unique value of the stress plateau of a highly sheared
viscoelastic fluid is stably realized. The present analysis is based on a
reduction theory of the degrees of freedom of the model equation in the
neighborhood of a critical point, which leads to a time-evolution equation that
is equivalent to those for first-order phase transitions.
