On Solvability of Systems of Symbolic Polynomial Equations

The theoretical description of the temperature field in the soils during freezing or thawing is carried out using solutions of Stefan's problem. A mathematical model based on the equations of thermal conductivity for frozen and thawed layers. We consider the areas in which there are lakes or bogs. We distinguished the following layers in the vertical structure of the zone of permafrost: thawed soil, frozen soil, water, ice, snow. We offer a simplified numerical algorithm for solving of one-dimensional (in the vertical direction) heat conduction problems with moving boundaries of phase transition with the formation of new and cancellation of existing layers. A simplified numerical algorithm for solving one-dimensional (in the vertical direction) heat conduction problems with moving boundaries of phase transition with the formation of new and cancellation of existing layers is offering.