Free boundary problem from stochastic lattice gas model

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7 Citations (Scopus)

Abstract

We consider a system consisting of two types of particles called "water" and "ice" on d-dimensional periodic lattices. The water particles perform excluded interacting random walks (stochastic lattice gases), while the ice particles are immobile. When a water particle touches an ice particle, it immediately dies. On the other hand, the ice particle disappears after receiving the ℓth visit from water particles. This interaction models the melting of a solid with latent heat. We derive the nonlinear one-phase Stefan free boundary problem in a hydrodynamic scaling limit. Derivation of two-phase Stefan problem is also discussed.

Original languageEnglish
Pages (from-to)573-603
Number of pages31
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Volume35
Issue number5
DOIs
Publication statusPublished - 1999 Sep
Externally publishedYes

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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