Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

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

 

 

The Stefan problem with small surface tension


Authors: Avner Friedman and Fernando Reitich
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 35R35, 35K20, 35K85

Retrieve articles in all journals with MSC: 35R35, 35K20, 35K85


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1991-1040260-9
Article copyright: © Copyright 1991 American Mathematical Society