On convergence of solutions of the crystalline Stefan problem with Gibbs-Thomson law and kinetic undercooling | Zendy

Piotr Rybka | Zendy

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On convergence of solutions of the crystalline Stefan problem with Gibbs-Thomson law and kinetic undercooling

Author(s) -

Piotr Rybka

Publication year - 2000

Publication title -

interfaces and free boundaries mathematical analysis computation and applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.964

H-Index - 39

eISSN - 1463-9971

pISSN - 1463-9963

DOI - 10.4171/ifb/25

Subject(s) - stefan problem , supercooling , convergence (economics) , regular polygon , plane (geometry) , polygon (computer graphics) , thermodynamics , mathematics , infinity , mathematical analysis , physics , geometry , computer science , economics , telecommunications , boundary (topology) , frame (networking) , economic growth

†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.

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