Geodesic
Regularity of expanding front and its application to solidification/melting in undercooled liquid/superheated solid
Xinfu Chen1 ; Huiqiang Jiang2
1University of Pittsburgh, United States
2University of Pittsburgh, USA
Interfaces and free boundaries, Tome 15 (2013) no. 3, pp. 281-322

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DOI

This article proves that fronts of expanding domains with Hölder continuous speeds are contained in finite unions of Lipschitz graphs. As an application, the global in time existence of a solution to a free boundary problem modelling solidification in undercooled liquid or liquidation in superheated solid is established; here the propagation speed of the liquid/solid interface is assumed to be a known positive smooth function of the temperature, known as a kinetic undercooling/superheating effect.
DOI : 10.4171/ifb/304
Classification : 35-XX, 80-XX
Mots-clés : Moving front, regularity, solidification, melting, undercooling, superheating

Xinfu Chen  1   ; Huiqiang Jiang  2

1 University of Pittsburgh, United States
2 University of Pittsburgh, USA 
Xinfu Chen; Huiqiang Jiang. Regularity of expanding front and its application to solidification/melting in undercooled liquid/superheated solid. Interfaces and free boundaries, Tome 15 (2013) no. 3, pp. 281-322. doi: 10.4171/ifb/304
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     title = {Regularity of expanding front and its application to solidification/melting in undercooled liquid/superheated solid},
     journal = {Interfaces and free boundaries},
     pages = {281--322},
     year = {2013},
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     number = {3},
     doi = {10.4171/ifb/304},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/304/}
}
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