On a one-phase transition problem of type ``solid body--compressible liquid'' (Q2713927)

The author presents new results on phase transitions of solid-liquid type with convection in the liquid phase. The characteristics of the liquid phase include the viscosity, compressibility, and thermal conductivity. Mathematically, the model looks like the one-phase Stefan problem and represents some generalization of this problem. These problems coincide when the liquid phase is stationary and the densities of the liquid and solid phases are equal to each other (and constant).NEWLINENEWLINENEWLINEThe aim of the article is to present an analytical study of the original problem. The author proves an existence and uniqueness result for a classical solution which is global in time in the case when the temperature of the solid phase equals the temperature of the so-called phase transition.