Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 

 

Vanishing specific heat for the classical solutions of a multidimensional Stefan problem with kinetic condition


Authors: Fahuai Yi and Jinduo Liu
Journal: Quart. Appl. Math. 57 (1999), 661-672
MSC: Primary 35R35; Secondary 35K05, 80A22
DOI: https://doi.org/10.1090/qam/1724298
MathSciNet review: MR1724298
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we prove that the multidimensional Hele-Shaw problem with kinetic condition at the free boundary is the limit case of the Stefan problem with kinetic condition at the free boundary in the classical sense when the specific heat $ \varepsilon $ goes to zero. The method is the use of a fixed point theorem; the key step is to construct a suitable function space in which we can get the existence and uniform estimates with respect to $ \varepsilon > 0$ at the same time as for classical solutions of the multidimensional Stefan problem with kinetic condition at the free boundary. For the sake of simplicity, we only consider one-phase problems in three space dimensions, although the method used here is also applicable for two-phase problems and any space dimensions.


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


Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 35R35, 35K05, 80A22

Retrieve articles in all journals with MSC: 35R35, 35K05, 80A22


Additional Information

DOI: https://doi.org/10.1090/qam/1724298
Article copyright: © Copyright 1999 American Mathematical Society


Brown University The Quarterly of Applied Mathematics
is distributed by the American Mathematical Society
for Brown University
Online ISSN 1552-4485; Print ISSN 0033-569X
© 2017 Brown University
Comments: qam-query@ams.org
AMS Website