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

Fast-reaction limit for Glauber-Kawasaki dynamics with two components