Free Boundary Problems in Solidification of Alloys
Vasilios Alexiades, John Rozier Cannon · SIAM Journal on Mathematical Analysis · 1980
Multidimensional three-phase free boundary problems for semilinear diffusion equations are studied as models for the solidification (or melting) of alloys. The intermediate phase represents the “mushy zone” in which the freezing of the remaining liquid provides a heat generation effect. The conditions on the two interfaces are of Stefan-type on one of them and of fast-chemical-reaction-type on the other. The existence, uniqueness and regularity of appropriately defined weak solutions are established when either the temperature or the heat flux is prescribed on the fixed boundary.