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Free boundary problem from stochastic lattice gas model. (English) Zbl 0935.60094

Summary: We consider a system consisting of two types of particles called “water” and “ice” on \(d\)-dimensional periodic lattices. The water particles perforn 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 \(l\)th 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.

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
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