Geodesic
On convergence of solutions of the crystalline Stefan problem with Gibbs-Thomson law and kinetic undercooling
Piotr Rybka1
1Warsaw University, Poland
Interfaces and free boundaries, Tome 2 (2000) no. 4, pp. 361-379

Voir la notice de l'article provenant de la source EMS Press

DOI

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.
DOI : 10.4171/ifb/25
Classification : 46-XX, 60-XX
Mots-clés : Free boundary, Stefan problem, Gibbs-Thomson law, crystalline anisotropy

Piotr Rybka  1

1 Warsaw University, Poland 
Piotr Rybka. On convergence of solutions of the crystalline Stefan problem with Gibbs-Thomson law and kinetic undercooling. Interfaces and free boundaries, Tome 2 (2000) no. 4, pp. 361-379. doi: 10.4171/ifb/25
@article{10_4171_ifb_25,
     author = {Piotr Rybka},
     title = {On convergence of solutions of the crystalline {Stefan} problem with {Gibbs-Thomson} law and kinetic undercooling},
     journal = {Interfaces and free boundaries},
     pages = {361--379},
     year = {2000},
     volume = {2},
     number = {4},
     doi = {10.4171/ifb/25},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/25/}
}
TY  - JOUR
AU  - Piotr Rybka
TI  - On convergence of solutions of the crystalline Stefan problem with Gibbs-Thomson law and kinetic undercooling
JO  - Interfaces and free boundaries
PY  - 2000
SP  - 361
EP  - 379
VL  - 2
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4171/ifb/25/
DO  - 10.4171/ifb/25
ID  - 10_4171_ifb_25
ER  - 
%0 Journal Article
%A Piotr Rybka
%T On convergence of solutions of the crystalline Stefan problem with Gibbs-Thomson law and kinetic undercooling
%J Interfaces and free boundaries
%D 2000
%P 361-379
%V 2
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4171/ifb/25/
%R 10.4171/ifb/25
%F 10_4171_ifb_25

Cité par Sources :