  The rigorous asymptotics from reaction-cross-diffusion systems for three
species with known entropy to cross-diffusion systems for two variables is
investigated. The equations are studied in a bounded domain with no-flux
boundary conditions. The global existence of very weak (integrable) solutions
and the rigorous fast-reaction limit are proved. The limiting system inherits
the entropy structure with an entropy that is not the sum of the entropies of
the components. Uniform estimates are derived from the entropy inequality and
the duality method.
