Fast-reaction limit for Glauber-Kawasaki dynamics with two components
Probability
2019-03-25 v1
Abstract
We consider the Kawasaki dynamics of two types of particles under a killing effect on a -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.
Cite
@article{arxiv.1903.09172,
title = {Fast-reaction limit for Glauber-Kawasaki dynamics with two components},
author = {Anna De Masi and Tadahisa Funaki and Errico Presutti and Maria Eulalia Vares},
journal= {arXiv preprint arXiv:1903.09172},
year = {2019}
}