On exact solutions of one-dimensional two phase free boundary problems for parabolic equations

The paper is concerned with auto-modelling solutions of one-dimensional two phase Stefan, Florin, and Verigin free boundary problems for parabolic equations whose initial and boundary data are not adjusted. It is shown that in the Stefan problem with “supercooling” a liquid can have a temperature less than the temperature of the phase transition, i.e., a liqued can be “supercooled” and solid “superheated.”