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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Free boundary convergence in the homogenization of the one-phase Stefan problem


Author: José-Francisco Rodrigues
Journal: Trans. Amer. Math. Soc. 274 (1982), 297-305
MSC: Primary 35R35; Secondary 35K05
DOI: https://doi.org/10.1090/S0002-9947-1982-0670933-3
MathSciNet review: 670933
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Abstract: We consider the one phase Stefan problem in a "granular" medium, i.e., with nonconstant thermal diffusity, and we study the asymptotic behaviour of the free boundary with respect to homogenization. We prove the convergence of the coincidence set in measure and in the Hausdorff metric. We apply this result to the free boundary and we obtain the convergence in mean for the star-shaped case and the uniform convergence for the one-dimensional case, respectively. This gives an answer to a problem posed by J. L. Lions in [L].


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DOI: https://doi.org/10.1090/S0002-9947-1982-0670933-3
Keywords: Free boundary problems, Parabolic variational inequalities, homogenization, Stefan problem
Article copyright: © Copyright 1982 American Mathematical Society