This paper presents a study of the relations between the modified Stefan problem in a plane and its quasi-steady approximation. In both cases the interfacial curve is assumed to be a polygon. It is shown that the weak solutions to the Stefan problem converge to weak solutions of the quasi-steady problem as the bulk specific heat tends to zero. The initial interface has to be convex of sufficiently small perimeter.
Julián Fernández Bonder; Noemi Wolanski. A free-boundary problem in combustion theory. Interfaces and free boundaries, Tome 2 (2000) no. 4, pp. 381-411. doi: 10.4171/ifb/26
@article{10_4171_ifb_26,
author = {Juli\'an Fern\'andez Bonder and Noemi Wolanski},
title = {A free-boundary problem in combustion theory},
journal = {Interfaces and free boundaries},
pages = {381--411},
year = {2000},
volume = {2},
number = {4},
doi = {10.4171/ifb/26},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/26/}
}
TY - JOUR
AU - Julián Fernández Bonder
AU - Noemi Wolanski
TI - A free-boundary problem in combustion theory
JO - Interfaces and free boundaries
PY - 2000
SP - 381
EP - 411
VL - 2
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.4171/ifb/26/
DO - 10.4171/ifb/26
ID - 10_4171_ifb_26
ER -
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%A Julián Fernández Bonder
%A Noemi Wolanski
%T A free-boundary problem in combustion theory
%J Interfaces and free boundaries
%D 2000
%P 381-411
%V 2
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4171/ifb/26/
%R 10.4171/ifb/26
%F 10_4171_ifb_26
