On the weak solutions for the multidimensional Stefan problem (Q910625)

This paper is concerned with weak solutions to the Stefan problem of parabolic differential equations for heat and mass diffusion in the solidifying three-phase mixture. The concentration of the mixture components is taken there into account. The scalar fields of temperature and concentration are interdependent at the Stefan boundary. The intermediary phase (called ``mushy zone'') between the liquid and the solid body is defined from one side by the Stefan boundary and from the other one by the so-called boundary of fast chemical reaction. The existence and uniqueness theorem of solutions to this problem is proved.