On the Stefan Problem with Different Phase Densities
V. N. Starovoîtov · ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik · 2000
A multidimensional problem concerning phase transitions of the liquid-liquid type in a moving substance with different phase densities is investigated. Rather special state equations are considered. The motion of the fluid is assumed to be slow. It is proved that the problem has a unique global solution. Also, some properties of the solution are investigated. It is shown that the mushy region does not increase in time. In the case of the one-phase Stefan problem the velocity of the substance is equal to zero in one of the two phases.