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De Masi, A.; Funaki, T.; Presutti, E.; Vares, M. E.

Fast-reaction limit for Glauber-Kawasaki dynamics with two components. (English) Zbl 1488.60229

ALEA, Lat. Am. J. Probab. Math. Stat. 16, No. 2, 957-976 (2019).
Summary: 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.

Cited in 6 Documents

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
35K55 Nonlinear parabolic equations
35K57 Reaction-diffusion equations
35R35 Free boundary problems for PDEs
80A22 Stefan problems, phase changes, etc.

Keywords:

hydrodynamical limit; relative entropy method; fast reaction limit; free boundary problem; singular limit problem
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References:

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