  We consider a finite number of particles that move in $\mathbb Z$ as
independent random walks. The particles are of two species that we call $a$ and
$b$. The rightmost $a$ particle becomes a $b$ particle at constant rate, while
the leftmost $b$ particle becomes $a$ particle at the same rate, independently.
We prove that in the hydrodynamic limit the evolution is described by a non
linear system of two PDE's with free boundaries.
