Editing Stefan problem (section)

{{Short description|Concept in mathematics}}
{{more citations needed|date=July 2013}}
In [[mathematics]] and its applications, particularly to [[phase transition]]s in matter, a '''Stefan problem''' is a particular kind of [[boundary value problem]] for a [[partial differential equation|system of partial differential equations]] (PDE), in which the boundary between the [[Phase (matter)|phases]] can move with time. The '''classical Stefan problem''' aims to describe the evolution of the boundary between two phases of a material undergoing a [[phase transition|phase change]], for example the melting of a solid, such as [[ice]] to [[water]].  This is accomplished by solving [[heat equation]]s in both regions, subject to given boundary and initial conditions. At the interface between the phases (in the classical problem) the temperature is set to the phase change temperature. To close the mathematical system a further equation, the '''Stefan condition''', is required. This is an energy balance which defines the position of the moving interface.  Note that this evolving boundary is an unknown [[hypersurface|(hyper-)surface]]; hence, Stefan problems are examples of [[free boundary problem]]s.

Analogous problems occur, for example, in the study of porous media flow, mathematical finance and crystal growth from monomer solutions.<ref>{{Cite book|title=Applied partial differential equations|date=2003|publisher=Oxford University Press|others=Ockendon, J. R.|isbn=0-19-852770-5|edition=Rev.|location=Oxford|oclc=52486357}}</ref>