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

A. de Masi, T. Funaki, E. Presutti, M. E. Vares

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

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.

Original languageEnglish
Pages (from-to)957-976
Number of pages20
JournalAlea
Volume16
Issue number2
DOIs
Publication statusPublished - 2019

Keywords

  • Fast reaction limit
  • Free boundary problem
  • Hydrodynamical limit
  • Relative entropy method
  • Singular limit problem

ASJC Scopus subject areas

  • Statistics and Probability

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