Free boundary problem from stochastic lattice gas model

T. Funaki

doi:10.1016/S0246-0203(99)00107-7

Free boundary problem from stochastic lattice gas model

T. Funaki^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

8 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 language	English
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
DOIs	https://doi.org/10.1016/S0246-0203(99)00107-7
Publication status	Published - 1999 Sept
Externally published	Yes

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1016/S0246-0203(99)00107-7

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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.

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Free boundary problem from stochastic lattice gas model

Abstract

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