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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Free boundary convergence in the homogenization of the one-phase Stefan problem
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by José-Francisco Rodrigues PDF
Trans. Amer. Math. Soc. 274 (1982), 297-305 Request permission

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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Additional Information
  • © Copyright 1982 American Mathematical Society
  • 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