Solvability of a Model Problem of Sublimation of Ice in Snow
Abstract
In this paper, a mathematical model of water and air motion in snow with consideration of a sublimation process is investigated. Snow is a porous medium with a solid frame of fixed ice particles. There are water, air, and steam in pores. The model utilizes a mass conservation equation for each phase, the Musket-Leverette equation system for water and air two-phase filtration, and the energy conservation equation for snow. The model is elaborated in Paragraph 1. Paragraph 2 presents the problem solution in self-similar variables. The problem is investigated in an infinite domain. Finite solutions are obtained for a field of velocities. The equation for temperature is presented, and monotony of the equation with an exponential approach to the target value at infinity is demonstrated. Also, the degenerate equation for water phase saturation and physical background for the maximum principle are provided. Solvability of the Cauchy problem is proved on the basis of this principle with an introduction of an additional parameter. The resulting solution is, firstly, expanded on a finite interval, and, later, on an infinite interval due to finite speed of disturbance propagation.
DOI 10.14258/izvasu(2017)1-23
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