  The present note deals with a nonstandard systems of differential equations
describing a two-species phase segregation. This system naturally arises in the
asymptotic analysis carried out recently by the same authors, as the diffusion
coefficient in the equation governing the evolution of the order parameter
tends to zero. In particular, an existence result has been proved for the limit
system in a very general framework. On the contrary, uniqueness was shown by
assuming a constant mobility coefficient. Here, we generalize this result and
prove a continuous dependence property in the case that the mobility
coefficient suitably depends on the chemical potential.
