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In mathematics and its applications, particularly to phase transitions in matter, a Stefan problem is a particular kind of boundary value problem for a system of partial differential equations (PDE), in which the boundary between the 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 change, for example the melting of a solid, such as ice to water. This is accomplished by solving heat equations 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 (hyper-)surface; hence, Stefan problems are examples of free boundary problems.
Analogous problems occur, for example, in the study of porous media flow, mathematical finance and crystal growth from monomer solutions.[1]
^Applied partial differential equations. Ockendon, J. R. (Rev. ed.). Oxford: Oxford University Press. 2003. ISBN 0-19-852770-5. OCLC 52486357.{{cite book}}: CS1 maint: others (link)
particularly to phase transitions in matter, a Stefanproblem is a particular kind of boundary value problem for a system of partial differential equations...
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Retrieved 7 September 2017. Glock, Stefan; Correia, David Munhá; Sudakov, Benny (6 July 2022). "The n-queens completion problem". Research in the Mathematical...
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American Petroleum Institute. p. 56. Hristov, Jordan (2006). "An Inverse StefanProblem Relevant to Boilover: Heat Balance Integral Solutions and Analysis"...
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