### 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 language | English |
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Pages (from-to) | 573-603 |

Number of pages | 31 |

Journal | Annales de l'institut Henri Poincare (B) Probability and Statistics |

Volume | 35 |

Issue number | 5 |

Publication status | Published - 1999 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty

### Cite this

**Free boundary problem from stochastic lattice gas model.** / Funaki, Tadahisa.

Research output: Contribution to journal › Article

*Annales de l'institut Henri Poincare (B) Probability and Statistics*, vol. 35, no. 5, pp. 573-603.

}

TY - JOUR

T1 - Free boundary problem from stochastic lattice gas model

AU - Funaki, Tadahisa

PY - 1999

Y1 - 1999

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0033194355&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033194355&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0033194355

VL - 35

SP - 573

EP - 603

JO - Annales de l'institut Henri Poincare (B) Probability and Statistics

JF - Annales de l'institut Henri Poincare (B) Probability and Statistics

SN - 0246-0203

IS - 5

ER -