Stefan problem
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In mathematics and its applications, particularly to phase transitions in matter, a Stefan problem (also Stefan task) is a particular kind of boundary value problem for a partial differential equation, adapted to the case in which a phase boundary can move with time. It is named for Jožef Stefan, the Slovene physicist who introduced the general class of such problems around 1890, in relation to problems of ice formation. This question had been considered earlier, in 1831, by Lamé and Clapeyron.
The Stefan problems are examples of free boundary problems, for parabolic equations. The Stefan condition is the expression in terms of temperature change of the conservation of energy, at the phase boundary.
