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

## TL;DR

This paper studies the large-scale behavior of a two-component particle system with killing interactions, showing that the interface evolution converges to a two-phase Stefan problem under diffusive scaling.

## Contribution

It establishes the hydrodynamic limit of the two-component Kawasaki dynamics with killing, linking microscopic particle interactions to a macroscopic PDE interface model.

## Key findings

- Segregation of particle types occurs over time.
- Interface evolution follows the two-phase Stefan problem.
- Method combines relative entropy with PDE techniques.

## Abstract

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.