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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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The Stefan problem with small surface tension
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by Avner Friedman and Fernando Reitich PDF
Trans. Amer. Math. Soc. 328 (1991), 465-515 Request permission

Abstract:

The Stefan problem with small surface tension $\varepsilon$ is considered. Assuming that the classical Stefan problem (with $\varepsilon = 0$) has a smooth free boundary $\Gamma$, we denote the temperature of the solution by ${\theta _0}$ and consider an approximate solution ${\theta _0} + \varepsilon u$ for the case where $\varepsilon \ne 0$, $\varepsilon$ small. We first establish the existence and uniqueness of $u$, and then investigate the effect of $u$ on the free boundary $\Gamma$. It is shown that small surface tension affects the free boundary $\Gamma$ radically differently in the two-phase problem than in the one-phase problem.
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Additional Information
  • © Copyright 1991 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 328 (1991), 465-515
  • MSC: Primary 35R35; Secondary 35K20, 35K85
  • DOI: https://doi.org/10.1090/S0002-9947-1991-1040260-9
  • MathSciNet review: 1040260