Editing Stefan problem (section)

==Applications==
Apart from modelling melting of solids, Stefan problem is also used as a model for the asymptotic behaviour (in time) of more complex problems. For example, Pego<ref name="Pego">R. L. Pego. (1989). Front Migration in the Nonlinear Cahn-Hilliard Equation. ''Proc. R. Soc. Lond. A.'','''422''':261&ndash;278.</ref> uses matched asymptotic expansions to prove that Cahn-Hilliard solutions for phase separation problems behave as solutions to a non-linear Stefan problem at an intermediate time scale. Additionally, the solution of the [[Cahn–Hilliard equation]] for a binary mixture is reasonably comparable with the solution of a Stefan problem.<ref>{{cite journal |first1=F. J. |last1=Vermolen |first2=M. G. |last2=Gharasoo |first3=P. L. J. |last3=Zitha |first4=J. |last4=Bruining |year=2009 |title=Numerical Solutions of Some Diffuse Interface Problems: The Cahn–Hilliard Equation and the Model of Thomas and Windle |journal=International Journal for Multiscale Computational Engineering |volume=7 |issue=6 |pages=523&ndash;543 |doi=10.1615/IntJMultCompEng.v7.i6.40 }}</ref> In this comparison, the Stefan problem was solved using a front-tracking, moving-mesh method with homogeneous [[Neumann boundary condition]]s at the outer boundary. Also, Stefan problems can be applied to describe phase transformations other than solid-fluid or fluid-fluid.<ref name=Alvarenga>{{cite journal |vauthors=Alvarenga HD, Van de Putter T, Van Steenberge N, Sietsma J, Terryn H |s2cid=136871961 |title=Influence of Carbide Morphology and Microstructure on the Kinetics of Superficial Decarburization of C-Mn Steels |journal= Metallurgical and Materials Transactions A|volume=46 |pages=123–133 |date=Apr 2009 |issue=1 |doi=10.1007/s11661-014-2600-y |bibcode = 2015MMTA...46..123A }}</ref>

Application of Stefan problem to metal crystallization in electrochemical deposition of metal powders was envisaged by Călușaru <ref>A. Călușaru, ''Electrochemical Deposition of Metal Powders'', Elsevier, Amsterdam,1978.</ref>

The Stefan problem also has a rich inverse theory; in such problems, the melting depth (or [[curve]] or [[hypersurface|hyper-surface]]) {{math|''s''}} is the known datum and the problem is to find {{math|''u''}} or {{math|''f''}}.<ref>{{harv|Kirsch|1996}}.</ref>