International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 3, Pages 549-563

The quasi-stationary approximation for the Stefan problem with a convective boundary condition

A. D. Solomon,1 D. G. Wilson,1 and V. Alexiades2

1Mathematics and Statistics Research Engineering, Physics and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge 37830, Tennessee, USA
2Department of Mathematics, The University of Tennessee, Knoxville 37996-1300, Tennessee, USA

Received 25 August 1983

Copyright © 1984 A. D. Solomon et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We show that the solution to the Stefan problem with a convective boundary condition tends to the quasi-stationary approximation as the specific heat tends to zero. Additional properties of the approximation are given, and some examples are presented.