  We consider the Kawasaki dynamics of two types of particles under a killing
effect on a $d$-dimensional square lattice. Particles move with possibly
different jump rates depending on their types. The killing effect acts when
particles of different types meet at the same site. We show the existence of a
limit under the diffusive space-time scaling and suitably growing killing rate:
segregation of distinct types of particles does occur, and the evolution of the
interface between the two distinct species is governed by the two-phase Stefan
problem. We apply the relative entropy method and combine it with some PDE
techniques.
