A microscopic model for Stefan’s melting and freezing problem

Claudio Landim; Glauco Valle

doi:10.1214/009117905000000701

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March 2006 A microscopic model for Stefan’s melting and freezing problem

Claudio Landim, Glauco Valle

Ann. Probab. 34(2): 779-803 (March 2006). DOI: 10.1214/009117905000000701

Abstract

We study a class of one-dimensional interacting particle systems with random boundaries as a microscopic model for Stefan’s melting and freezing problem. We prove that under diffusive rescaling these particle systems exhibit a hydrodynamic behavior described by the solution of a Cauchy–Stefan problem.

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Claudio Landim. Glauco Valle. "A microscopic model for Stefan’s melting and freezing problem." Ann. Probab. 34 (2) 779 - 803, March 2006. https://doi.org/10.1214/009117905000000701